Original Article

Proc IMechE Part DJ Automobile Engineering1ndash12 IMechE 2017Reprints and permissionssagepubcoukjournalsPermissionsnavDOI 1011770954407017707670journalssagepubcomhomepid

Experimental vibro-acoustic analysis ofthe gear rattle induced by multi-harmonicexcitation

Renato Brancati1 Ernesto Rocca1 Daniela Siano2 andMassimo Viscardi1

AbstractThe paper reports a wide vibro-acoustic experimental investigation of the gear rattle phenomenon induced by multi-harmonic excitation The analysis is performed by using different measurement techniques which allow some of the sig-nificant parameters in this type of investigation to be acquired on a specific test rig the angular rotations of the gears byusing encoders the accelerations obtained from a triaxial accelerometer the sound pressure level determined byemploying both acoustic microphones the correct evaluation of the acoustic sources by utilizing a pndashv sound intensityprobe Performance indices were adopted to compare the dynamic behaviours of the system with respect to some para-meters such as the speed of the pinion the fluctuations in the speed of the pinion and the lubrication conditions Theresults of the comparative analysis show very good agreement between the vibro-acoustic measurements and the resultsfrom the encoder-based method this has helped us to interpret the physical behaviour of the gear pair with respect tothe impacts occurring between the teeth during the different phases of the phenomenon Moreover the study indicatesinteresting aspects of the effects of multi-harmonic excitation on the rattle phenomenon with particular attention tothe influence of lubrication on the reduction in the rattle noise

KeywordsGear rattle noise vibration acoustic measurements

Date received 27 July 2016 accepted 14 March 2017

Introduction

Gear rattle is a typical vibro-acoustic phenomenon ofthe automotive gearbox it represents today an annoy-ing problem for the car industry with regard to theacoustic comfort and therefore is strictly related to thequality of the product1ndash3

Gear rattle is caused by fluctuations in the torque ofthe alternative engine these produce consequent speedfluctuations which cause repetitive impacts between theteeth of unloaded gear pairs in the gearbox12 The fre-quency of these speed fluctuations at the primary shaftof the gearbox depends on the number of cylinders andon the engine technology45 As an example in a four-stroke four-cylinder engine the ignition frequencywhich is double that of the rotation frequency charac-terizes the rattle cycle More precisely because of thediscontinuous combustion in the engine the excitationof the input shaft is of the periodic type with a funda-mental frequency which is the same as that of theignition

This research topic has been mainly studied by theo-retical and experimental approaches and various meth-odologies have been adopted Many theoretical studiesdeal with the torsional analysis of the entire driveline toreduce the rattle noise by design modifications In theexperimental field the investigations often consist inanalysing a specific automotive gearbox which is mon-itored by acoustic microphones or instrumented withaccelerometers to acquire the overall vibration level

Other experimental approaches in this field are basedon the relief of the relative angular displacements of thegears by using encoders57 The above technique is gen-erally used to analyse the errors and the discontinuities

1Department of Industrial Engineering University of Naples Federico II

Naples Italy2Istituto Motori ndash Consiglio Nazionale delle Ricerche Naples Italy

Corresponding author

Renato Brancati Department of Industrial Engineering University of

Naples Federico II Naples Italy

Email renatobrancatiuninait

in the contacts between the gear teeth or to acquiresome kinematic quantities such as the eccentricity ofthe wheels or the effective backlashes which are usefulto characterize the dynamic behaviour of the gearsThis approach is suitable in particular to use in thediagnostics of gears

Although in the literature many studies have consid-ered the gear rattle generally forced by harmonic excita-tions in the present paper a more realistic excitation ofthe multi-harmonic type is applied2

In particular the excitation consists of the sum oftwo harmonic components using the law of the pinionspeed Much attention was placed on determining athreshold for the onset of the gear rattle in particularby comparing the acoustic noise radiated from a mesh-ing gear pair with the data analysed in the frequencydomain which were acquired by an encoder-basedmethodology

Another aspect examined in the present analysis con-siders the operative conditions of the gear pair in termsof the lubrication and in particular the influence of theoil between the teeth during the impacts This effect iswell known in the literature7ndash11 because the presence ofa lubricant in the impact phases acts as a damper byattenuating the gear rattle noise

Experimental test rig

The experimental test rig consists of a helical spur gearthe pinion of which is driven by a speed-controlledbrushless motor with a maximum output torqueof 22 N m The motor speed controller enables anacceptable speedndashtime history to be found for the gearpair

Apart from the negligible drag torque due to thebearings no load is applied to the secondary shaft

Therefore the test rig simulates lsquoidlersquo operatingconditions

The rig is instrumented to measure some mechanicalquantities which are useful for performing a vibroacous-tic analysis of the system In particular the measuredparameters are as follows the angular rotations of thegears by using encoders the accelerations along threedifferent directions from a triaxial accelerometer thesound pressure level by employing microphones Thegear pair used for the present analysis is characterizedby a transmission ratio e = z2z1 = 3337 = 089 Forthe present tests the distance between the axes was fixedat 655 mm In this configuration the measured angularbacklash has a mean value of about 101 3 10ndash4 radwith a periodic fluctuation ranging between a minimumvalue of 86 3 10ndash5 rad and a maximum of 117 3 10ndash4

rad owing to assembly and manufacturing errorsVibrational and acoustic analyses were performed

by integrating complementary instrumentation deviceswith the aim of correlating the causes and the effects inorder to determine the airborne or structure-bornenoise transmission paths more effectively A near-fieldacoustic sensor was used for complete scanning of thegear area to localize the noise sources satisfactorilyFigure 1 shows the test set-up

The experimental equipment consists of thefollowing

(a) pressure transducers (PCB class 1 ICPmicrophone)

(b) a PCB triaxial accelerometer(c) two optical encoders(d) a multi-channel fast Fourier transform (FFT) ana-

lyser (LMS Siemens Scadas acquisition system)(e) pre-processing software and post-processing soft-

ware (LMS TestLab) for sound pressure levelmeasurements

Figure 1 Instrumented rig

2 Proc IMechE Part D J Automobile Engineering

Multi-harmonic excitation

The gear rattle noise is caused by oscillations of theangular speed induced by the irregularities of the enginetorque For this reason as an excitation a periodicspeed law with two harmonic components was consid-ered which is given by

O(t)=Om +A1 sin (2pft)+A2 sin (4pft) eth1THORN

where Om is the mean value of the speed A1 andA2 are the amplitudes of the speed fluctuation compo-nents and f is the fundamental frequency of the rattlecycle

The experimental tests were carried out for threemean speed values Om =500 rmin 600 rmin and 700rmin The fundamental component A1 has an ampli-tude equal to 20 of the mean speed because it approx-imates in practice the speed irregularities of theautomotive reciprocating engines the amplitude of thesecond-order component A2 ranges from 20 up to100 of the A1 component The value of the funda-mental frequency of rattle is f= 5 Hz for all the tests

The experiments were performed under two lubrica-tion conditions namely dry lubrication and boundarylubrication Dry lubrication was tested for use as a ref-erence In this case no oil was used for the gears Theboundary lubrication consists of limited lubricationwhich is characterized by a thin oil film on the flanksof each tooth without any external oil feeding The oiladopted for the tests has the following characteristicsSAE grade 80w90 test temperature 20 C dynamicviscosity approximately 035 Pa s

Experimental results

In the following some experimental results arereported with reference to the various measurementstechniques adopted for the investigation angularmotion measurements vibration measurements andnear-field and far-field acoustic measurements

Angular motion measurements

The time histories of the relative angular motions of thegears are acquired by the use of two incremental enco-ders with a high resolution fixed to each shaft The res-olution of the encoders is equal to 10000 pulsesrev oneach channel By virtue of quadrature detection eachencoder provides therefore a resolution of 40000pulsesrev

The speed law (1) was imposed at the pinion gear Inorder to demonstrate that the desired speed law is cor-rectly reproduced Figure 2 shows the waterfall spectraup to 40 Hz measured by the pinion gear encoderThese spectra are for the case when the mean speed Om

= 500 rmin and A1 = 100 rmin for various second-order harmonic amplitude values

The transmission error (TE) which is defined as therelative angular motion Du(t) is measured by

combining the two absolute rotations u1 and u2 of thegears according to

Du(t)= u1(t) u2(t)r2r1

= u1(t) u2(t)z2z1

where r1 is the pitch radius of the pinion gear r2 is thepitch radius of the wheel gear z1 is the number of teethon the pinion gear and z2 is the number of teeth on thewheel gear

Figure 3 shows the TE and its FFT in the case of thepinion gear with a constant speed equal to 500 rminThis case is reported as a reference to highlight the har-monic content of the pure rotations without consider-ing any fluctuations in the speed The frequencycomponents of the pinion gear rotations and the wheelgear rotations are evident in the diagrams In fact twomajor components can be observed namely 833 Hzand 934 Hz together with their ultra-harmonic compo-nents In particular the 934 Hz component appears tobe more pronounced than the 833 Hz componentbecause of the presence of a tooth defect observed onthe wheel gear this is evidenced also by the spikes inthe TE diagram

Figure 4 shows the TEs and the FFTs for the casesof the first harmonic component equal to 100 rmin fora mean speed of 500 rmin and for the second-orderharmonic equal to 0 rmin 50 rmin 80 rmin and 100rmin respectively It is interesting to note that the FFTshows that the first harmonic of the relative motion ini-tially increases and then decreases when the second-order excitation A2 exceeds the value of 50 rminMoreover the second-order component of the TE con-stantly increases when the second-order excitationincreases

Vibration measurements

Vibrational levels which are acquired by using thetriaxial accelerometer in the proximity of the driven-wheel shaft support (Figure 1) were investigated in

Figure 2 Harmonic components of the measured imposedmotions (Om = 500 rmin)FFT fast Fourier transform rpm rmin

Brancati et al 3

terms of both the overall levels of acceleration and thespectral characteristics

As appears evident from Figure 5 a generalizedincrease in the overall levels of vibrations can be notedas the second-order harmonic increases the maximumvibration levels are along the y axis (the transverseaxis)

It is also interesting to observe the positive effect ofthe oil lubrication which strongly reduces the overallvibration levels Figure 6 shows with reference to the

case when Om = 500 rmin the x-axis the y-axis andthe z-axis vibration spectra as functions of the second-order harmonic of the excitation It is confirmed thatthe vibrations along the y axis have a much largeramplitude than do the amplitudes for the other axesTherefore there is a negligible level of high-frequencyvibrations along the z axis The comparisons of spectraalong the y axis clearly highlight the increase in the fun-damental frequency together with increases in its upperharmonics

Figure 3 TE and FFT for the constant speed Om = 500 rminTE transmission error

Figure 4 TE and FFT for Om = 500 rmin and various A2 amplitude values (a) A2 =0 rmin (b) A2 =50 rmin (c) A2 =80 rmin(d) A2 =100 rminTE transmission error

4 Proc IMechE Part D J Automobile Engineering

In the waterfall x-axis spectrum a high level ofvibrations can be observed for the frequencies near 600Hz which are due to the gear teeth meshing With

respect to the y-axis spectra components are present ataround 2500 Hz which are caused by some structuralresonances of the test rig

Figure 5 Overall vibrational levels along the x axis and the y axis as functions of the second-order harmonic A2rpm rmin

Figure 6 Vibration spectra as functions of the second-order harmonic A2 (Om = 500 rmin)

Brancati et al 5

Near-field acoustic measurements

All the acoustic measurements are evaluated in terms ofthe relative values for the different operative conditionsmore than in terms of the absolute values this consider-ation is strictly related to the characteristics of the testenvironment (semi-reverberant) which cannot beassimilated to any of the standard acoustic test environ-ments (ie anechoic semi-anechoic or reverberant)

To justify this limitation a particle velocity measure-ment technique was therefore introduced Sound-pres-sure-based measurement methods and processingtechniques often fail to provide appropriate results insuch conditions owing to the high levels of backgroundnoise Alternatively maps of the particle velocity allowthe acoustic excitations to be characterized across thesystem despite measurement in the harsh environmentMore precisely near-field experiments were performedby using novel instrumentation with the employment ofa particle velocity sensor (Microflown) TheMicroflown acoustic sensor measures the velocity12 ofair lsquoparticlesrsquo across two tiny resistive strips of platinumwhich are heated to about 300 C The temperaturechange due to a particular vibration close to the systemunder test is measured with a bridge circuit which pro-vides a signal proportional to the acoustic particle velo-city This particle velocity sensor is usually mountedtogether with a pressure microphone on a sound inten-sity pndashu probe When the particle velocity (sound) pro-pagates orthogonally across the wires it asymmetricallyalters the temperature distribution around the resistorsThe resulting resistance difference provides a broad-band (0 Hz up to at least 20 kHz) linear signal that isproportional to the particle velocity up to sound levelsof 135 dB The reliability of measuring the sound levelfrom particle velocity measurements close to rigidboundaries is well known and also in the presence ofother external sources in fact in near-field measure-ments the contributions from other directions arestrongly reduced

The measurement procedure to acquire thedata is based upon the scanning technique lsquoscan andpaintrsquo13

The displacement of the Microflown pndashu probe wasrecorded by a camera placed perpendicular to the testbench measurement area so as to avoid any visualerrors caused by the camera projection A gear rattlescan was performed by moving the sensor close to thesurface of the system The camera recorded the displa-cement of the probe using discretization with about 150points for each operating condition Each scanning ses-sion lasted about 1 min The experimental acquisitionswere processed in the frequency range 20ndash5000 Hz Theresults are combined with a background picture of themeasured environment to obtain a visual representa-tion which allows the noise source to be visualized andidentified

Figure 7 shows for Om =500 rmin A1 = 100 rmin and A2 = 70 rmin the normal particle velocityand the sound pressure maps in dry-lubrication condi-tions The velocity vector was then measured using theparticle velocity sensor and the velocity surface distri-bution in the near field can be visualized as a contourmap expressed in decibels (ie 5 310ndash8 ms) to detectlocalization of the sound sources Because the particlevelocity is a vector it is sensitive to the wave directionand the pndashu configuration provides a powerful combi-nation for suppressing extraneous noise and reflectionsduring its application

As can be seen by comparing the particle velocityand the pressure maps no sound sources external to thegears can be identified on the pressure map The reasonis that the background noise which is caused by soundsources distributed across the system is masking thedirect pressure emitted by specific areas of the vibratingstructure in contrast with the situation when viewingthe particle velocity maps It may be deduced that thegear system presents in the evaluated frequency banda most powerful excitation source which corresponds tothe gears

Figure 8(a) and (b) shows a comparison of thedirecty mapping for Om = 600 rmin A1 = 120 rminand A2 = 60 rmin in the cases of dry lubrication andboundary lubrication respectively It can be seen thatthe normal particle velocity maps for the two different

Figure 7 Direct mapping of the gear system for (a) the sound pressure and (b) the particle velocity for Om = 500 rminA1 =100 rmin and A2 =70 rmin

6 Proc IMechE Part D J Automobile Engineering

lubrication conditions highlight the positive effect oflubrication

The method to visualize and map the results in thisway represents intuitive feedback from the measure-ments allowing the noise sources across an unknownsound field to be easily localized

Figure 9 and Figure 10 show comparisons of thepressure velocity spectra with the lubricant and withoutthe lubricant respectively For Figure 9 Om = 500rmin A1 = 100 rmin and A2 =70 rmin whereas forFigure 10 Om = 600rmin A1 = 120 rmin and A2 =60 rmin The results reveal a noise source with twodominant peaks at about 300 Hz and 600 Hz whichrepresent the fundamental frequency and the second-order frequency respectively of the gear meshing Thepresence of oil reduces the noise emitted by the systemachieving about 10 dB in some frequency bands

Far-field acoustic measurements

In the present section the results of the sound pressureanalysis by employing microphones is reported Timendashfrequency graphs in the dry-lubrication conditions areshown in Figure 11 and provide evidence of the station-ary characteristics of the phenomena

An analysis of the overall levels also shows as previ-ously verified for vibrational signals an increase in theacoustic sound level as a function of the second-orderharmonic amplitude In Figure 12 the microphone over-all levels for the three mean speed values of 500 rmin600 rmin and 700 rmin for both lubrication operatingconditions are shown The far-field measurements tech-nique also reveals a sensitivity to the effect of the lubri-cant in reducing the gear rattle noise level

In Figure 13 the waterfall spectra of acoustic signalsare shown for the cases of dry lubrication and boundarylubrication respectively

From an acoustic viewpoint the frequency ranges ofmajor interest are those shown in Figure 14 iebetween 450 Hz and 750 Hz where the amplitude ofthe signals is more evident This figure shows the spec-tra of the microphone measurements for different val-ues of the average speed and different amplitudes ofthe second harmonic for dry-lubrication conditions Itcan be seen that an increase in the A2 component valuecauses an increase in the acoustic sound level

As already stated with respect to the accelerometerresults the frequencies near 600 Hz are due to themeshing of gear teeth in particular they represent thesecond-order component of the meshing frequency

Figure 8 Direct mapping of the gear system for the particle velocity for Om = 600 rmin A1 = 120 rmin and A2 = 60 rmin in thecases of (a) dry lubrication and (b) boundary lubrication

Figure 9 Comparison of the pressure velocity level spectrafor Om = 500 rmin A1 =100 rmin and A2 = 70 rmin with oil(open squares) and without oil (open circles)PVL pressure velocity level

Figure 10 Comparison of the pressure velocity level spectrafor Om = 600 rmin A1 = 120 rmin and A2 = 60 rmin with oil(open circles) and without oil (open squares)PVL pressure velocity level

Brancati et al 7

Figure 15 shows the sound level in the above fre-quency ranges for the two mean speed values of 500 rmin and 700 rmin where the effect of oil can beobserved by comparing the diagrams for the differentlubrication conditions

Gear rattle index

A gear rattle index (IGR) has been defined in previouswork and is adopted in order to compare and discrimi-nate in an objective way between different vibro-acoustic behaviours caused by different excitationsand also by different lubrication conditions The IGRwhich is referred to as the relative angular motion Du

of the gears is defined as the value of the integral714

between 20 Hz and 5000 Hz according to

IGR=

eth5000 Hz

20 Hz

Du veth THORNj j dv eth2THORN

In the present analysis the index was evaluated for theexperimental signals from the encoders for the spectrafrom the accelerometer measurements and for the spec-tra from the acoustic sound measurements

Figures 16 17 and 18 show the values of the IGRcalculated with reference to the above-mentionedexperimental measurements

It should be noted that the IGR metric gives reliableinformation with regard to the vibro-acoustic beha-viour independently of the adopted measurement meth-odology In fact the index gives qualitativelyanalogous results of the analysis performed by theencoders ie it increases with increasing A2 excitationcomponent Moreover the index includes the positiveeffect due to the oil in reducing the rattle

Conclusion

In this paper an experimental analysis of the gear rattlephenomenon was presented using a correlation between

Figure 11 Acoustic waterfall spectra versus time (dry-lubrication conditions Om = 500 rmin A1 = 100 rmin)mic microphone rpm rmin

Figure 12 Overall vibrational levelsMic microphone rpm rmin

8 Proc IMechE Part D J Automobile Engineering

Figure 13 Waterfall spectra of the acoustic signalsmic microphone rpm rmin

Figure 14 Acoustic sound level spectra for the 450ndash750 Hz rangemic microphone rpm rmin

Brancati et al 9

different measurement methodologies for the acousticsound emissions the levels of vibrations and the angu-lar motions of the gears

The study was performed on a dedicated test set-upwhere the rattle phenomenon was induced throughmulti-harmonic excitation with two components forwhich the second-order component amplitude was var-ied in particular

The acquisition of the sound pressure level fromacoustic microphones was supported by an investiga-tion with a pndashv sound intensity probe for correctevaluation of the near-field acoustic sourcesThe vibro-acoustic analysis showed notable results about thecorrelation with the encoder-based methodology whichenables an accurate analysis of the tooth contacts andimpacts occurring during the rattle to be made From

Figure 15 Sound spectra comparisons for two lubrication conditionsmic microphone rpm rmin

Figure 16 IGR for the encoder measurementsIGR gear rattle index rpm rmin

10 Proc IMechE Part D J Automobile Engineering

an acoustic viewpoint the analysis not only demon-strates that the lubricant always plays a positive role inthe reduction of the rattle noise but also shows that thepresence of the second harmonic in the excitation stillcauses an increase in the acoustic noise level In partic-ular the microphone measurements highlighted that

the second harmonic of the excitation amplifies the fre-quencies around 600 Hz (near to the second order ofgear meshing) The results of the pndashv acoustic investiga-tion instead reveal a dominant noise source in the fre-quency range 250ndash750 Hz with two dominant peakscorresponding to about 300 Hz and 600 Hz which

Figure 17 IGR for the accelerometer measurementss along the x axisIGR gear rattle index rpm rmin

Figure 18 IGR for the acoustic sound measurementsIGR gear rattle index rpm rmin

Brancati et al 11

represent the gear-meshing frequency and its second-order component respectively

The qualitative good agreement between the differ-ent methodologies was confirmed also by a perfor-mance index developed by the present authors on thebasis of the harmonic analysis of data

Although each measurement technique provides spe-cific information on the behaviour of the gears thepresent investigation makes it clear that depending onthe particular needs of the researcher it is possible toachieve similar results from a qualitative point of viewusing any one of the proposed methodologies

Acknowledgements

The authors thank Gennaro Stingo and GiuseppeIovino of the Department of Industrial EngineeringUniversity of Naples Federico II for their fundamentaltechnical support during the tuning stages of the testrig

Declaration of conflicting interests

The author(s) declared no potential conflicts of interestwith respect to the research authorship andor publi-cation of this article

Funding

The author(s) disclosed receipt of the following finan-cial support for the research authorship andor publi-cation of this article This research received no specificgrant from any funding agency in the public commer-cial or not-for-profit sectors

References

1 Wang Y Manoj R and Zhao W J Gear rattle modelingand analysis for automotive manual transmissions ProcIMechE Part D J Automobile Engineering 2001 215(2)

241ndash2582 Barthod M Hayne B Tebec JL et al Experimental study

of gear rattle excited by a multi- harmonic excitationAppl Acoust 2007 68(9) 1003ndash1025

3 Dogan S N Ryborz J and Bertsche B Design of low-noise manual automotive transmissions Proc IMechE

Part K J Multi-body Dynamics 2006 220(2) 79ndash954 Brancati R Rocca E Savino S et al Experimental analy-

sis of the relative motion of a gear pair under rattle con-ditions induced by multi-harmonic excitation In World

congress on engineering London UK 1ndash3 July 2015 pp1016ndash1021 London IAENG

5 Younes K Rigaud E Perret-Liaudet J et al Experimen-tal and numerical analysis of automotive gearbox rattlenoise J Sound Vibr 2012 331(13) 3144ndash3157

6 Brancati R Montanaro U Rocca E et al Analysis ofbifurcations rattle and chaos in a gear transmission sys-tem Int Rev Mech Engng 2013 7(4) 583ndash591

7 Rocca E and Russo R Theoretical and experimentalinvestigation into the influence of the periodic backlashfluctuations on the gear rattle J Sound Vibr 2011330(20) 4738ndash4752

8 Brancati R Rocca E and Russo R A gear rattle modelaccounting for oil squeeze between the meshing gearteeth Proc IMechE Part D J Automobile Engineering2005 219(9) 1075ndash1083

9 De la Cruz M Theodossiades S and Rahnejat H Aninvestigation of manual transmission drive rattle ProcIMechE Part K J Multi-body Dynamics 2010 224(2)167ndash181

10 Theodossiades S De la Cruz M and Rahnejat H Predic-tion of airborne radiated noise from lightly loaded lubri-cated meshing gear teeth Appl Acoust 2015 100 79ndash86

11 Brancati R Rocca E and Russo R An analysis of theautomotive driveline dynamic behaviour focusing on theinfluence of the oil squeeze effect on the idle rattle phe-nomenon J Sound Vibr 2007 303(3ndash5) 858ndash872

12 Siano D Viscardi M and Panza A Experimental acousticmeasurements in far field and near field conditions char-acterization of a beauty engine cover In 12th interna-tional conference on fluid mechanics and aerodynamics and12th international conference on heat transfer thermalengineering and environment Geneva Switzerland 29ndash31December 2014 pp 50ndash57 Geneva WSEAS

13 Siano D Viscardi M and Aiello R Experimental andnumerical validation of an automotive subsystem throughthe employment of FEMBEM approaches Energy Pro-cedia 2015 82 67ndash74

14 Brancati R Rocca E Lauria D Feasibility study of theHilbert transform in detecting the gear rattle phenom-enon of automotive transmissions Journal of Vibrationand Control prepublished February 1 2017 DOI1011771077546316689745

Appendix 1Notation

Ai amplitudes of the speed fluctuationcomponents (i = 1 2)

f fundamental frequency of the rattle cycler1 pitch radius of the pinion gearr2 pitch radius of the wheel gearz1 number of teeth on the pinion gearz2 number of teeth on the wheel gear

Du transmission errore transmission ratioui absolute rotations of the gears (i = 1 2)O angular speedOm mean value of the angular speed

12 Proc IMechE Part D J Automobile Engineering

Multi-harmonic excitation

The gear rattle noise is caused by oscillations of theangular speed induced by the irregularities of the enginetorque For this reason as an excitation a periodicspeed law with two harmonic components was consid-ered which is given by

O(t)=Om +A1 sin (2pft)+A2 sin (4pft) eth1THORN

where Om is the mean value of the speed A1 andA2 are the amplitudes of the speed fluctuation compo-nents and f is the fundamental frequency of the rattlecycle

The experimental tests were carried out for threemean speed values Om =500 rmin 600 rmin and 700rmin The fundamental component A1 has an ampli-tude equal to 20 of the mean speed because it approx-imates in practice the speed irregularities of theautomotive reciprocating engines the amplitude of thesecond-order component A2 ranges from 20 up to100 of the A1 component The value of the funda-mental frequency of rattle is f= 5 Hz for all the tests

The experiments were performed under two lubrica-tion conditions namely dry lubrication and boundarylubrication Dry lubrication was tested for use as a ref-erence In this case no oil was used for the gears Theboundary lubrication consists of limited lubricationwhich is characterized by a thin oil film on the flanksof each tooth without any external oil feeding The oiladopted for the tests has the following characteristicsSAE grade 80w90 test temperature 20 C dynamicviscosity approximately 035 Pa s

Experimental results

In the following some experimental results arereported with reference to the various measurementstechniques adopted for the investigation angularmotion measurements vibration measurements andnear-field and far-field acoustic measurements

Angular motion measurements

The time histories of the relative angular motions of thegears are acquired by the use of two incremental enco-ders with a high resolution fixed to each shaft The res-olution of the encoders is equal to 10000 pulsesrev oneach channel By virtue of quadrature detection eachencoder provides therefore a resolution of 40000pulsesrev

The speed law (1) was imposed at the pinion gear Inorder to demonstrate that the desired speed law is cor-rectly reproduced Figure 2 shows the waterfall spectraup to 40 Hz measured by the pinion gear encoderThese spectra are for the case when the mean speed Om

= 500 rmin and A1 = 100 rmin for various second-order harmonic amplitude values

The transmission error (TE) which is defined as therelative angular motion Du(t) is measured by

combining the two absolute rotations u1 and u2 of thegears according to

Du(t)= u1(t) u2(t)r2r1

= u1(t) u2(t)z2z1

where r1 is the pitch radius of the pinion gear r2 is thepitch radius of the wheel gear z1 is the number of teethon the pinion gear and z2 is the number of teeth on thewheel gear

Figure 3 shows the TE and its FFT in the case of thepinion gear with a constant speed equal to 500 rminThis case is reported as a reference to highlight the har-monic content of the pure rotations without consider-ing any fluctuations in the speed The frequencycomponents of the pinion gear rotations and the wheelgear rotations are evident in the diagrams In fact twomajor components can be observed namely 833 Hzand 934 Hz together with their ultra-harmonic compo-nents In particular the 934 Hz component appears tobe more pronounced than the 833 Hz componentbecause of the presence of a tooth defect observed onthe wheel gear this is evidenced also by the spikes inthe TE diagram

Figure 4 shows the TEs and the FFTs for the casesof the first harmonic component equal to 100 rmin fora mean speed of 500 rmin and for the second-orderharmonic equal to 0 rmin 50 rmin 80 rmin and 100rmin respectively It is interesting to note that the FFTshows that the first harmonic of the relative motion ini-tially increases and then decreases when the second-order excitation A2 exceeds the value of 50 rminMoreover the second-order component of the TE con-stantly increases when the second-order excitationincreases

Vibration measurements

Vibrational levels which are acquired by using thetriaxial accelerometer in the proximity of the driven-wheel shaft support (Figure 1) were investigated in

Figure 2 Harmonic components of the measured imposedmotions (Om = 500 rmin)FFT fast Fourier transform rpm rmin

Brancati et al 3

terms of both the overall levels of acceleration and thespectral characteristics

As appears evident from Figure 5 a generalizedincrease in the overall levels of vibrations can be notedas the second-order harmonic increases the maximumvibration levels are along the y axis (the transverseaxis)

It is also interesting to observe the positive effect ofthe oil lubrication which strongly reduces the overallvibration levels Figure 6 shows with reference to the

case when Om = 500 rmin the x-axis the y-axis andthe z-axis vibration spectra as functions of the second-order harmonic of the excitation It is confirmed thatthe vibrations along the y axis have a much largeramplitude than do the amplitudes for the other axesTherefore there is a negligible level of high-frequencyvibrations along the z axis The comparisons of spectraalong the y axis clearly highlight the increase in the fun-damental frequency together with increases in its upperharmonics

Figure 3 TE and FFT for the constant speed Om = 500 rminTE transmission error

Figure 4 TE and FFT for Om = 500 rmin and various A2 amplitude values (a) A2 =0 rmin (b) A2 =50 rmin (c) A2 =80 rmin(d) A2 =100 rminTE transmission error

4 Proc IMechE Part D J Automobile Engineering

In the waterfall x-axis spectrum a high level ofvibrations can be observed for the frequencies near 600Hz which are due to the gear teeth meshing With

respect to the y-axis spectra components are present ataround 2500 Hz which are caused by some structuralresonances of the test rig

Figure 5 Overall vibrational levels along the x axis and the y axis as functions of the second-order harmonic A2rpm rmin

Figure 6 Vibration spectra as functions of the second-order harmonic A2 (Om = 500 rmin)

Brancati et al 5

Near-field acoustic measurements

All the acoustic measurements are evaluated in terms ofthe relative values for the different operative conditionsmore than in terms of the absolute values this consider-ation is strictly related to the characteristics of the testenvironment (semi-reverberant) which cannot beassimilated to any of the standard acoustic test environ-ments (ie anechoic semi-anechoic or reverberant)

To justify this limitation a particle velocity measure-ment technique was therefore introduced Sound-pres-sure-based measurement methods and processingtechniques often fail to provide appropriate results insuch conditions owing to the high levels of backgroundnoise Alternatively maps of the particle velocity allowthe acoustic excitations to be characterized across thesystem despite measurement in the harsh environmentMore precisely near-field experiments were performedby using novel instrumentation with the employment ofa particle velocity sensor (Microflown) TheMicroflown acoustic sensor measures the velocity12 ofair lsquoparticlesrsquo across two tiny resistive strips of platinumwhich are heated to about 300 C The temperaturechange due to a particular vibration close to the systemunder test is measured with a bridge circuit which pro-vides a signal proportional to the acoustic particle velo-city This particle velocity sensor is usually mountedtogether with a pressure microphone on a sound inten-sity pndashu probe When the particle velocity (sound) pro-pagates orthogonally across the wires it asymmetricallyalters the temperature distribution around the resistorsThe resulting resistance difference provides a broad-band (0 Hz up to at least 20 kHz) linear signal that isproportional to the particle velocity up to sound levelsof 135 dB The reliability of measuring the sound levelfrom particle velocity measurements close to rigidboundaries is well known and also in the presence ofother external sources in fact in near-field measure-ments the contributions from other directions arestrongly reduced

The measurement procedure to acquire thedata is based upon the scanning technique lsquoscan andpaintrsquo13

The displacement of the Microflown pndashu probe wasrecorded by a camera placed perpendicular to the testbench measurement area so as to avoid any visualerrors caused by the camera projection A gear rattlescan was performed by moving the sensor close to thesurface of the system The camera recorded the displa-cement of the probe using discretization with about 150points for each operating condition Each scanning ses-sion lasted about 1 min The experimental acquisitionswere processed in the frequency range 20ndash5000 Hz Theresults are combined with a background picture of themeasured environment to obtain a visual representa-tion which allows the noise source to be visualized andidentified

Figure 7 shows for Om =500 rmin A1 = 100 rmin and A2 = 70 rmin the normal particle velocityand the sound pressure maps in dry-lubrication condi-tions The velocity vector was then measured using theparticle velocity sensor and the velocity surface distri-bution in the near field can be visualized as a contourmap expressed in decibels (ie 5 310ndash8 ms) to detectlocalization of the sound sources Because the particlevelocity is a vector it is sensitive to the wave directionand the pndashu configuration provides a powerful combi-nation for suppressing extraneous noise and reflectionsduring its application

As can be seen by comparing the particle velocityand the pressure maps no sound sources external to thegears can be identified on the pressure map The reasonis that the background noise which is caused by soundsources distributed across the system is masking thedirect pressure emitted by specific areas of the vibratingstructure in contrast with the situation when viewingthe particle velocity maps It may be deduced that thegear system presents in the evaluated frequency banda most powerful excitation source which corresponds tothe gears

Figure 8(a) and (b) shows a comparison of thedirecty mapping for Om = 600 rmin A1 = 120 rminand A2 = 60 rmin in the cases of dry lubrication andboundary lubrication respectively It can be seen thatthe normal particle velocity maps for the two different

Figure 7 Direct mapping of the gear system for (a) the sound pressure and (b) the particle velocity for Om = 500 rminA1 =100 rmin and A2 =70 rmin

6 Proc IMechE Part D J Automobile Engineering

lubrication conditions highlight the positive effect oflubrication

The method to visualize and map the results in thisway represents intuitive feedback from the measure-ments allowing the noise sources across an unknownsound field to be easily localized

Figure 9 and Figure 10 show comparisons of thepressure velocity spectra with the lubricant and withoutthe lubricant respectively For Figure 9 Om = 500rmin A1 = 100 rmin and A2 =70 rmin whereas forFigure 10 Om = 600rmin A1 = 120 rmin and A2 =60 rmin The results reveal a noise source with twodominant peaks at about 300 Hz and 600 Hz whichrepresent the fundamental frequency and the second-order frequency respectively of the gear meshing Thepresence of oil reduces the noise emitted by the systemachieving about 10 dB in some frequency bands

Far-field acoustic measurements

In the present section the results of the sound pressureanalysis by employing microphones is reported Timendashfrequency graphs in the dry-lubrication conditions areshown in Figure 11 and provide evidence of the station-ary characteristics of the phenomena

An analysis of the overall levels also shows as previ-ously verified for vibrational signals an increase in theacoustic sound level as a function of the second-orderharmonic amplitude In Figure 12 the microphone over-all levels for the three mean speed values of 500 rmin600 rmin and 700 rmin for both lubrication operatingconditions are shown The far-field measurements tech-nique also reveals a sensitivity to the effect of the lubri-cant in reducing the gear rattle noise level

In Figure 13 the waterfall spectra of acoustic signalsare shown for the cases of dry lubrication and boundarylubrication respectively

From an acoustic viewpoint the frequency ranges ofmajor interest are those shown in Figure 14 iebetween 450 Hz and 750 Hz where the amplitude ofthe signals is more evident This figure shows the spec-tra of the microphone measurements for different val-ues of the average speed and different amplitudes ofthe second harmonic for dry-lubrication conditions Itcan be seen that an increase in the A2 component valuecauses an increase in the acoustic sound level

As already stated with respect to the accelerometerresults the frequencies near 600 Hz are due to themeshing of gear teeth in particular they represent thesecond-order component of the meshing frequency

Figure 8 Direct mapping of the gear system for the particle velocity for Om = 600 rmin A1 = 120 rmin and A2 = 60 rmin in thecases of (a) dry lubrication and (b) boundary lubrication

Figure 9 Comparison of the pressure velocity level spectrafor Om = 500 rmin A1 =100 rmin and A2 = 70 rmin with oil(open squares) and without oil (open circles)PVL pressure velocity level

Figure 10 Comparison of the pressure velocity level spectrafor Om = 600 rmin A1 = 120 rmin and A2 = 60 rmin with oil(open circles) and without oil (open squares)PVL pressure velocity level

Brancati et al 7

Figure 15 shows the sound level in the above fre-quency ranges for the two mean speed values of 500 rmin and 700 rmin where the effect of oil can beobserved by comparing the diagrams for the differentlubrication conditions

Gear rattle index

A gear rattle index (IGR) has been defined in previouswork and is adopted in order to compare and discrimi-nate in an objective way between different vibro-acoustic behaviours caused by different excitationsand also by different lubrication conditions The IGRwhich is referred to as the relative angular motion Du

of the gears is defined as the value of the integral714

between 20 Hz and 5000 Hz according to

IGR=

eth5000 Hz

20 Hz

Du veth THORNj j dv eth2THORN

In the present analysis the index was evaluated for theexperimental signals from the encoders for the spectrafrom the accelerometer measurements and for the spec-tra from the acoustic sound measurements

Figures 16 17 and 18 show the values of the IGRcalculated with reference to the above-mentionedexperimental measurements

It should be noted that the IGR metric gives reliableinformation with regard to the vibro-acoustic beha-viour independently of the adopted measurement meth-odology In fact the index gives qualitativelyanalogous results of the analysis performed by theencoders ie it increases with increasing A2 excitationcomponent Moreover the index includes the positiveeffect due to the oil in reducing the rattle

Conclusion

In this paper an experimental analysis of the gear rattlephenomenon was presented using a correlation between

Figure 11 Acoustic waterfall spectra versus time (dry-lubrication conditions Om = 500 rmin A1 = 100 rmin)mic microphone rpm rmin

Figure 12 Overall vibrational levelsMic microphone rpm rmin

8 Proc IMechE Part D J Automobile Engineering

Figure 13 Waterfall spectra of the acoustic signalsmic microphone rpm rmin

Figure 14 Acoustic sound level spectra for the 450ndash750 Hz rangemic microphone rpm rmin

Brancati et al 9

different measurement methodologies for the acousticsound emissions the levels of vibrations and the angu-lar motions of the gears

The study was performed on a dedicated test set-upwhere the rattle phenomenon was induced throughmulti-harmonic excitation with two components forwhich the second-order component amplitude was var-ied in particular

The acquisition of the sound pressure level fromacoustic microphones was supported by an investiga-tion with a pndashv sound intensity probe for correctevaluation of the near-field acoustic sourcesThe vibro-acoustic analysis showed notable results about thecorrelation with the encoder-based methodology whichenables an accurate analysis of the tooth contacts andimpacts occurring during the rattle to be made From

Figure 15 Sound spectra comparisons for two lubrication conditionsmic microphone rpm rmin

Figure 16 IGR for the encoder measurementsIGR gear rattle index rpm rmin

10 Proc IMechE Part D J Automobile Engineering

an acoustic viewpoint the analysis not only demon-strates that the lubricant always plays a positive role inthe reduction of the rattle noise but also shows that thepresence of the second harmonic in the excitation stillcauses an increase in the acoustic noise level In partic-ular the microphone measurements highlighted that

the second harmonic of the excitation amplifies the fre-quencies around 600 Hz (near to the second order ofgear meshing) The results of the pndashv acoustic investiga-tion instead reveal a dominant noise source in the fre-quency range 250ndash750 Hz with two dominant peakscorresponding to about 300 Hz and 600 Hz which

Figure 17 IGR for the accelerometer measurementss along the x axisIGR gear rattle index rpm rmin

Figure 18 IGR for the acoustic sound measurementsIGR gear rattle index rpm rmin

Brancati et al 11

represent the gear-meshing frequency and its second-order component respectively

The qualitative good agreement between the differ-ent methodologies was confirmed also by a perfor-mance index developed by the present authors on thebasis of the harmonic analysis of data

Although each measurement technique provides spe-cific information on the behaviour of the gears thepresent investigation makes it clear that depending onthe particular needs of the researcher it is possible toachieve similar results from a qualitative point of viewusing any one of the proposed methodologies

Acknowledgements

The authors thank Gennaro Stingo and GiuseppeIovino of the Department of Industrial EngineeringUniversity of Naples Federico II for their fundamentaltechnical support during the tuning stages of the testrig

Declaration of conflicting interests

The author(s) declared no potential conflicts of interestwith respect to the research authorship andor publi-cation of this article

Funding

The author(s) disclosed receipt of the following finan-cial support for the research authorship andor publi-cation of this article This research received no specificgrant from any funding agency in the public commer-cial or not-for-profit sectors

References

1 Wang Y Manoj R and Zhao W J Gear rattle modelingand analysis for automotive manual transmissions ProcIMechE Part D J Automobile Engineering 2001 215(2)

241ndash2582 Barthod M Hayne B Tebec JL et al Experimental study

of gear rattle excited by a multi- harmonic excitationAppl Acoust 2007 68(9) 1003ndash1025

3 Dogan S N Ryborz J and Bertsche B Design of low-noise manual automotive transmissions Proc IMechE

Part K J Multi-body Dynamics 2006 220(2) 79ndash954 Brancati R Rocca E Savino S et al Experimental analy-

sis of the relative motion of a gear pair under rattle con-ditions induced by multi-harmonic excitation In World

congress on engineering London UK 1ndash3 July 2015 pp1016ndash1021 London IAENG

5 Younes K Rigaud E Perret-Liaudet J et al Experimen-tal and numerical analysis of automotive gearbox rattlenoise J Sound Vibr 2012 331(13) 3144ndash3157

6 Brancati R Montanaro U Rocca E et al Analysis ofbifurcations rattle and chaos in a gear transmission sys-tem Int Rev Mech Engng 2013 7(4) 583ndash591

7 Rocca E and Russo R Theoretical and experimentalinvestigation into the influence of the periodic backlashfluctuations on the gear rattle J Sound Vibr 2011330(20) 4738ndash4752

8 Brancati R Rocca E and Russo R A gear rattle modelaccounting for oil squeeze between the meshing gearteeth Proc IMechE Part D J Automobile Engineering2005 219(9) 1075ndash1083

9 De la Cruz M Theodossiades S and Rahnejat H Aninvestigation of manual transmission drive rattle ProcIMechE Part K J Multi-body Dynamics 2010 224(2)167ndash181

10 Theodossiades S De la Cruz M and Rahnejat H Predic-tion of airborne radiated noise from lightly loaded lubri-cated meshing gear teeth Appl Acoust 2015 100 79ndash86

11 Brancati R Rocca E and Russo R An analysis of theautomotive driveline dynamic behaviour focusing on theinfluence of the oil squeeze effect on the idle rattle phe-nomenon J Sound Vibr 2007 303(3ndash5) 858ndash872

12 Siano D Viscardi M and Panza A Experimental acousticmeasurements in far field and near field conditions char-acterization of a beauty engine cover In 12th interna-tional conference on fluid mechanics and aerodynamics and12th international conference on heat transfer thermalengineering and environment Geneva Switzerland 29ndash31December 2014 pp 50ndash57 Geneva WSEAS

13 Siano D Viscardi M and Aiello R Experimental andnumerical validation of an automotive subsystem throughthe employment of FEMBEM approaches Energy Pro-cedia 2015 82 67ndash74

14 Brancati R Rocca E Lauria D Feasibility study of theHilbert transform in detecting the gear rattle phenom-enon of automotive transmissions Journal of Vibrationand Control prepublished February 1 2017 DOI1011771077546316689745

Appendix 1Notation

Ai amplitudes of the speed fluctuationcomponents (i = 1 2)

f fundamental frequency of the rattle cycler1 pitch radius of the pinion gearr2 pitch radius of the wheel gearz1 number of teeth on the pinion gearz2 number of teeth on the wheel gear

Du transmission errore transmission ratioui absolute rotations of the gears (i = 1 2)O angular speedOm mean value of the angular speed

12 Proc IMechE Part D J Automobile Engineering

terms of both the overall levels of acceleration and thespectral characteristics

As appears evident from Figure 5 a generalizedincrease in the overall levels of vibrations can be notedas the second-order harmonic increases the maximumvibration levels are along the y axis (the transverseaxis)

It is also interesting to observe the positive effect ofthe oil lubrication which strongly reduces the overallvibration levels Figure 6 shows with reference to the

case when Om = 500 rmin the x-axis the y-axis andthe z-axis vibration spectra as functions of the second-order harmonic of the excitation It is confirmed thatthe vibrations along the y axis have a much largeramplitude than do the amplitudes for the other axesTherefore there is a negligible level of high-frequencyvibrations along the z axis The comparisons of spectraalong the y axis clearly highlight the increase in the fun-damental frequency together with increases in its upperharmonics

Figure 3 TE and FFT for the constant speed Om = 500 rminTE transmission error

Figure 4 TE and FFT for Om = 500 rmin and various A2 amplitude values (a) A2 =0 rmin (b) A2 =50 rmin (c) A2 =80 rmin(d) A2 =100 rminTE transmission error

4 Proc IMechE Part D J Automobile Engineering

In the waterfall x-axis spectrum a high level ofvibrations can be observed for the frequencies near 600Hz which are due to the gear teeth meshing With

respect to the y-axis spectra components are present ataround 2500 Hz which are caused by some structuralresonances of the test rig

Figure 5 Overall vibrational levels along the x axis and the y axis as functions of the second-order harmonic A2rpm rmin

Figure 6 Vibration spectra as functions of the second-order harmonic A2 (Om = 500 rmin)

Brancati et al 5

Near-field acoustic measurements

All the acoustic measurements are evaluated in terms ofthe relative values for the different operative conditionsmore than in terms of the absolute values this consider-ation is strictly related to the characteristics of the testenvironment (semi-reverberant) which cannot beassimilated to any of the standard acoustic test environ-ments (ie anechoic semi-anechoic or reverberant)

To justify this limitation a particle velocity measure-ment technique was therefore introduced Sound-pres-sure-based measurement methods and processingtechniques often fail to provide appropriate results insuch conditions owing to the high levels of backgroundnoise Alternatively maps of the particle velocity allowthe acoustic excitations to be characterized across thesystem despite measurement in the harsh environmentMore precisely near-field experiments were performedby using novel instrumentation with the employment ofa particle velocity sensor (Microflown) TheMicroflown acoustic sensor measures the velocity12 ofair lsquoparticlesrsquo across two tiny resistive strips of platinumwhich are heated to about 300 C The temperaturechange due to a particular vibration close to the systemunder test is measured with a bridge circuit which pro-vides a signal proportional to the acoustic particle velo-city This particle velocity sensor is usually mountedtogether with a pressure microphone on a sound inten-sity pndashu probe When the particle velocity (sound) pro-pagates orthogonally across the wires it asymmetricallyalters the temperature distribution around the resistorsThe resulting resistance difference provides a broad-band (0 Hz up to at least 20 kHz) linear signal that isproportional to the particle velocity up to sound levelsof 135 dB The reliability of measuring the sound levelfrom particle velocity measurements close to rigidboundaries is well known and also in the presence ofother external sources in fact in near-field measure-ments the contributions from other directions arestrongly reduced

The measurement procedure to acquire thedata is based upon the scanning technique lsquoscan andpaintrsquo13

The displacement of the Microflown pndashu probe wasrecorded by a camera placed perpendicular to the testbench measurement area so as to avoid any visualerrors caused by the camera projection A gear rattlescan was performed by moving the sensor close to thesurface of the system The camera recorded the displa-cement of the probe using discretization with about 150points for each operating condition Each scanning ses-sion lasted about 1 min The experimental acquisitionswere processed in the frequency range 20ndash5000 Hz Theresults are combined with a background picture of themeasured environment to obtain a visual representa-tion which allows the noise source to be visualized andidentified

Figure 7 shows for Om =500 rmin A1 = 100 rmin and A2 = 70 rmin the normal particle velocityand the sound pressure maps in dry-lubrication condi-tions The velocity vector was then measured using theparticle velocity sensor and the velocity surface distri-bution in the near field can be visualized as a contourmap expressed in decibels (ie 5 310ndash8 ms) to detectlocalization of the sound sources Because the particlevelocity is a vector it is sensitive to the wave directionand the pndashu configuration provides a powerful combi-nation for suppressing extraneous noise and reflectionsduring its application

As can be seen by comparing the particle velocityand the pressure maps no sound sources external to thegears can be identified on the pressure map The reasonis that the background noise which is caused by soundsources distributed across the system is masking thedirect pressure emitted by specific areas of the vibratingstructure in contrast with the situation when viewingthe particle velocity maps It may be deduced that thegear system presents in the evaluated frequency banda most powerful excitation source which corresponds tothe gears

Figure 8(a) and (b) shows a comparison of thedirecty mapping for Om = 600 rmin A1 = 120 rminand A2 = 60 rmin in the cases of dry lubrication andboundary lubrication respectively It can be seen thatthe normal particle velocity maps for the two different

Figure 7 Direct mapping of the gear system for (a) the sound pressure and (b) the particle velocity for Om = 500 rminA1 =100 rmin and A2 =70 rmin

6 Proc IMechE Part D J Automobile Engineering

lubrication conditions highlight the positive effect oflubrication

The method to visualize and map the results in thisway represents intuitive feedback from the measure-ments allowing the noise sources across an unknownsound field to be easily localized

Figure 9 and Figure 10 show comparisons of thepressure velocity spectra with the lubricant and withoutthe lubricant respectively For Figure 9 Om = 500rmin A1 = 100 rmin and A2 =70 rmin whereas forFigure 10 Om = 600rmin A1 = 120 rmin and A2 =60 rmin The results reveal a noise source with twodominant peaks at about 300 Hz and 600 Hz whichrepresent the fundamental frequency and the second-order frequency respectively of the gear meshing Thepresence of oil reduces the noise emitted by the systemachieving about 10 dB in some frequency bands

Far-field acoustic measurements

In the present section the results of the sound pressureanalysis by employing microphones is reported Timendashfrequency graphs in the dry-lubrication conditions areshown in Figure 11 and provide evidence of the station-ary characteristics of the phenomena

An analysis of the overall levels also shows as previ-ously verified for vibrational signals an increase in theacoustic sound level as a function of the second-orderharmonic amplitude In Figure 12 the microphone over-all levels for the three mean speed values of 500 rmin600 rmin and 700 rmin for both lubrication operatingconditions are shown The far-field measurements tech-nique also reveals a sensitivity to the effect of the lubri-cant in reducing the gear rattle noise level

In Figure 13 the waterfall spectra of acoustic signalsare shown for the cases of dry lubrication and boundarylubrication respectively

From an acoustic viewpoint the frequency ranges ofmajor interest are those shown in Figure 14 iebetween 450 Hz and 750 Hz where the amplitude ofthe signals is more evident This figure shows the spec-tra of the microphone measurements for different val-ues of the average speed and different amplitudes ofthe second harmonic for dry-lubrication conditions Itcan be seen that an increase in the A2 component valuecauses an increase in the acoustic sound level

As already stated with respect to the accelerometerresults the frequencies near 600 Hz are due to themeshing of gear teeth in particular they represent thesecond-order component of the meshing frequency

Figure 8 Direct mapping of the gear system for the particle velocity for Om = 600 rmin A1 = 120 rmin and A2 = 60 rmin in thecases of (a) dry lubrication and (b) boundary lubrication

Figure 9 Comparison of the pressure velocity level spectrafor Om = 500 rmin A1 =100 rmin and A2 = 70 rmin with oil(open squares) and without oil (open circles)PVL pressure velocity level

Figure 10 Comparison of the pressure velocity level spectrafor Om = 600 rmin A1 = 120 rmin and A2 = 60 rmin with oil(open circles) and without oil (open squares)PVL pressure velocity level

Brancati et al 7

Figure 15 shows the sound level in the above fre-quency ranges for the two mean speed values of 500 rmin and 700 rmin where the effect of oil can beobserved by comparing the diagrams for the differentlubrication conditions

Gear rattle index

A gear rattle index (IGR) has been defined in previouswork and is adopted in order to compare and discrimi-nate in an objective way between different vibro-acoustic behaviours caused by different excitationsand also by different lubrication conditions The IGRwhich is referred to as the relative angular motion Du

of the gears is defined as the value of the integral714

between 20 Hz and 5000 Hz according to

IGR=

eth5000 Hz

20 Hz

Du veth THORNj j dv eth2THORN

In the present analysis the index was evaluated for theexperimental signals from the encoders for the spectrafrom the accelerometer measurements and for the spec-tra from the acoustic sound measurements

Figures 16 17 and 18 show the values of the IGRcalculated with reference to the above-mentionedexperimental measurements

It should be noted that the IGR metric gives reliableinformation with regard to the vibro-acoustic beha-viour independently of the adopted measurement meth-odology In fact the index gives qualitativelyanalogous results of the analysis performed by theencoders ie it increases with increasing A2 excitationcomponent Moreover the index includes the positiveeffect due to the oil in reducing the rattle

Conclusion

In this paper an experimental analysis of the gear rattlephenomenon was presented using a correlation between

Figure 11 Acoustic waterfall spectra versus time (dry-lubrication conditions Om = 500 rmin A1 = 100 rmin)mic microphone rpm rmin

Figure 12 Overall vibrational levelsMic microphone rpm rmin

8 Proc IMechE Part D J Automobile Engineering

Figure 13 Waterfall spectra of the acoustic signalsmic microphone rpm rmin

Figure 14 Acoustic sound level spectra for the 450ndash750 Hz rangemic microphone rpm rmin

Brancati et al 9

different measurement methodologies for the acousticsound emissions the levels of vibrations and the angu-lar motions of the gears

The study was performed on a dedicated test set-upwhere the rattle phenomenon was induced throughmulti-harmonic excitation with two components forwhich the second-order component amplitude was var-ied in particular

The acquisition of the sound pressure level fromacoustic microphones was supported by an investiga-tion with a pndashv sound intensity probe for correctevaluation of the near-field acoustic sourcesThe vibro-acoustic analysis showed notable results about thecorrelation with the encoder-based methodology whichenables an accurate analysis of the tooth contacts andimpacts occurring during the rattle to be made From

Figure 15 Sound spectra comparisons for two lubrication conditionsmic microphone rpm rmin

Figure 16 IGR for the encoder measurementsIGR gear rattle index rpm rmin

10 Proc IMechE Part D J Automobile Engineering

an acoustic viewpoint the analysis not only demon-strates that the lubricant always plays a positive role inthe reduction of the rattle noise but also shows that thepresence of the second harmonic in the excitation stillcauses an increase in the acoustic noise level In partic-ular the microphone measurements highlighted that

the second harmonic of the excitation amplifies the fre-quencies around 600 Hz (near to the second order ofgear meshing) The results of the pndashv acoustic investiga-tion instead reveal a dominant noise source in the fre-quency range 250ndash750 Hz with two dominant peakscorresponding to about 300 Hz and 600 Hz which

Figure 17 IGR for the accelerometer measurementss along the x axisIGR gear rattle index rpm rmin

Figure 18 IGR for the acoustic sound measurementsIGR gear rattle index rpm rmin

Brancati et al 11

represent the gear-meshing frequency and its second-order component respectively

The qualitative good agreement between the differ-ent methodologies was confirmed also by a perfor-mance index developed by the present authors on thebasis of the harmonic analysis of data

Although each measurement technique provides spe-cific information on the behaviour of the gears thepresent investigation makes it clear that depending onthe particular needs of the researcher it is possible toachieve similar results from a qualitative point of viewusing any one of the proposed methodologies

Acknowledgements

The authors thank Gennaro Stingo and GiuseppeIovino of the Department of Industrial EngineeringUniversity of Naples Federico II for their fundamentaltechnical support during the tuning stages of the testrig

Declaration of conflicting interests

The author(s) declared no potential conflicts of interestwith respect to the research authorship andor publi-cation of this article

Funding

The author(s) disclosed receipt of the following finan-cial support for the research authorship andor publi-cation of this article This research received no specificgrant from any funding agency in the public commer-cial or not-for-profit sectors

References

1 Wang Y Manoj R and Zhao W J Gear rattle modelingand analysis for automotive manual transmissions ProcIMechE Part D J Automobile Engineering 2001 215(2)

241ndash2582 Barthod M Hayne B Tebec JL et al Experimental study

of gear rattle excited by a multi- harmonic excitationAppl Acoust 2007 68(9) 1003ndash1025

3 Dogan S N Ryborz J and Bertsche B Design of low-noise manual automotive transmissions Proc IMechE

Part K J Multi-body Dynamics 2006 220(2) 79ndash954 Brancati R Rocca E Savino S et al Experimental analy-

sis of the relative motion of a gear pair under rattle con-ditions induced by multi-harmonic excitation In World

congress on engineering London UK 1ndash3 July 2015 pp1016ndash1021 London IAENG

5 Younes K Rigaud E Perret-Liaudet J et al Experimen-tal and numerical analysis of automotive gearbox rattlenoise J Sound Vibr 2012 331(13) 3144ndash3157

6 Brancati R Montanaro U Rocca E et al Analysis ofbifurcations rattle and chaos in a gear transmission sys-tem Int Rev Mech Engng 2013 7(4) 583ndash591

7 Rocca E and Russo R Theoretical and experimentalinvestigation into the influence of the periodic backlashfluctuations on the gear rattle J Sound Vibr 2011330(20) 4738ndash4752

8 Brancati R Rocca E and Russo R A gear rattle modelaccounting for oil squeeze between the meshing gearteeth Proc IMechE Part D J Automobile Engineering2005 219(9) 1075ndash1083

9 De la Cruz M Theodossiades S and Rahnejat H Aninvestigation of manual transmission drive rattle ProcIMechE Part K J Multi-body Dynamics 2010 224(2)167ndash181

10 Theodossiades S De la Cruz M and Rahnejat H Predic-tion of airborne radiated noise from lightly loaded lubri-cated meshing gear teeth Appl Acoust 2015 100 79ndash86

11 Brancati R Rocca E and Russo R An analysis of theautomotive driveline dynamic behaviour focusing on theinfluence of the oil squeeze effect on the idle rattle phe-nomenon J Sound Vibr 2007 303(3ndash5) 858ndash872

12 Siano D Viscardi M and Panza A Experimental acousticmeasurements in far field and near field conditions char-acterization of a beauty engine cover In 12th interna-tional conference on fluid mechanics and aerodynamics and12th international conference on heat transfer thermalengineering and environment Geneva Switzerland 29ndash31December 2014 pp 50ndash57 Geneva WSEAS

13 Siano D Viscardi M and Aiello R Experimental andnumerical validation of an automotive subsystem throughthe employment of FEMBEM approaches Energy Pro-cedia 2015 82 67ndash74

14 Brancati R Rocca E Lauria D Feasibility study of theHilbert transform in detecting the gear rattle phenom-enon of automotive transmissions Journal of Vibrationand Control prepublished February 1 2017 DOI1011771077546316689745

Appendix 1Notation

Ai amplitudes of the speed fluctuationcomponents (i = 1 2)

f fundamental frequency of the rattle cycler1 pitch radius of the pinion gearr2 pitch radius of the wheel gearz1 number of teeth on the pinion gearz2 number of teeth on the wheel gear

Du transmission errore transmission ratioui absolute rotations of the gears (i = 1 2)O angular speedOm mean value of the angular speed

12 Proc IMechE Part D J Automobile Engineering

In the waterfall x-axis spectrum a high level ofvibrations can be observed for the frequencies near 600Hz which are due to the gear teeth meshing With

respect to the y-axis spectra components are present ataround 2500 Hz which are caused by some structuralresonances of the test rig

Figure 5 Overall vibrational levels along the x axis and the y axis as functions of the second-order harmonic A2rpm rmin

Figure 6 Vibration spectra as functions of the second-order harmonic A2 (Om = 500 rmin)

Brancati et al 5

Near-field acoustic measurements

All the acoustic measurements are evaluated in terms ofthe relative values for the different operative conditionsmore than in terms of the absolute values this consider-ation is strictly related to the characteristics of the testenvironment (semi-reverberant) which cannot beassimilated to any of the standard acoustic test environ-ments (ie anechoic semi-anechoic or reverberant)

To justify this limitation a particle velocity measure-ment technique was therefore introduced Sound-pres-sure-based measurement methods and processingtechniques often fail to provide appropriate results insuch conditions owing to the high levels of backgroundnoise Alternatively maps of the particle velocity allowthe acoustic excitations to be characterized across thesystem despite measurement in the harsh environmentMore precisely near-field experiments were performedby using novel instrumentation with the employment ofa particle velocity sensor (Microflown) TheMicroflown acoustic sensor measures the velocity12 ofair lsquoparticlesrsquo across two tiny resistive strips of platinumwhich are heated to about 300 C The temperaturechange due to a particular vibration close to the systemunder test is measured with a bridge circuit which pro-vides a signal proportional to the acoustic particle velo-city This particle velocity sensor is usually mountedtogether with a pressure microphone on a sound inten-sity pndashu probe When the particle velocity (sound) pro-pagates orthogonally across the wires it asymmetricallyalters the temperature distribution around the resistorsThe resulting resistance difference provides a broad-band (0 Hz up to at least 20 kHz) linear signal that isproportional to the particle velocity up to sound levelsof 135 dB The reliability of measuring the sound levelfrom particle velocity measurements close to rigidboundaries is well known and also in the presence ofother external sources in fact in near-field measure-ments the contributions from other directions arestrongly reduced

The measurement procedure to acquire thedata is based upon the scanning technique lsquoscan andpaintrsquo13

The displacement of the Microflown pndashu probe wasrecorded by a camera placed perpendicular to the testbench measurement area so as to avoid any visualerrors caused by the camera projection A gear rattlescan was performed by moving the sensor close to thesurface of the system The camera recorded the displa-cement of the probe using discretization with about 150points for each operating condition Each scanning ses-sion lasted about 1 min The experimental acquisitionswere processed in the frequency range 20ndash5000 Hz Theresults are combined with a background picture of themeasured environment to obtain a visual representa-tion which allows the noise source to be visualized andidentified

Figure 7 shows for Om =500 rmin A1 = 100 rmin and A2 = 70 rmin the normal particle velocityand the sound pressure maps in dry-lubrication condi-tions The velocity vector was then measured using theparticle velocity sensor and the velocity surface distri-bution in the near field can be visualized as a contourmap expressed in decibels (ie 5 310ndash8 ms) to detectlocalization of the sound sources Because the particlevelocity is a vector it is sensitive to the wave directionand the pndashu configuration provides a powerful combi-nation for suppressing extraneous noise and reflectionsduring its application

As can be seen by comparing the particle velocityand the pressure maps no sound sources external to thegears can be identified on the pressure map The reasonis that the background noise which is caused by soundsources distributed across the system is masking thedirect pressure emitted by specific areas of the vibratingstructure in contrast with the situation when viewingthe particle velocity maps It may be deduced that thegear system presents in the evaluated frequency banda most powerful excitation source which corresponds tothe gears

Figure 8(a) and (b) shows a comparison of thedirecty mapping for Om = 600 rmin A1 = 120 rminand A2 = 60 rmin in the cases of dry lubrication andboundary lubrication respectively It can be seen thatthe normal particle velocity maps for the two different

Figure 7 Direct mapping of the gear system for (a) the sound pressure and (b) the particle velocity for Om = 500 rminA1 =100 rmin and A2 =70 rmin

6 Proc IMechE Part D J Automobile Engineering

lubrication conditions highlight the positive effect oflubrication

The method to visualize and map the results in thisway represents intuitive feedback from the measure-ments allowing the noise sources across an unknownsound field to be easily localized

Figure 9 and Figure 10 show comparisons of thepressure velocity spectra with the lubricant and withoutthe lubricant respectively For Figure 9 Om = 500rmin A1 = 100 rmin and A2 =70 rmin whereas forFigure 10 Om = 600rmin A1 = 120 rmin and A2 =60 rmin The results reveal a noise source with twodominant peaks at about 300 Hz and 600 Hz whichrepresent the fundamental frequency and the second-order frequency respectively of the gear meshing Thepresence of oil reduces the noise emitted by the systemachieving about 10 dB in some frequency bands

Far-field acoustic measurements

In the present section the results of the sound pressureanalysis by employing microphones is reported Timendashfrequency graphs in the dry-lubrication conditions areshown in Figure 11 and provide evidence of the station-ary characteristics of the phenomena

An analysis of the overall levels also shows as previ-ously verified for vibrational signals an increase in theacoustic sound level as a function of the second-orderharmonic amplitude In Figure 12 the microphone over-all levels for the three mean speed values of 500 rmin600 rmin and 700 rmin for both lubrication operatingconditions are shown The far-field measurements tech-nique also reveals a sensitivity to the effect of the lubri-cant in reducing the gear rattle noise level

In Figure 13 the waterfall spectra of acoustic signalsare shown for the cases of dry lubrication and boundarylubrication respectively

From an acoustic viewpoint the frequency ranges ofmajor interest are those shown in Figure 14 iebetween 450 Hz and 750 Hz where the amplitude ofthe signals is more evident This figure shows the spec-tra of the microphone measurements for different val-ues of the average speed and different amplitudes ofthe second harmonic for dry-lubrication conditions Itcan be seen that an increase in the A2 component valuecauses an increase in the acoustic sound level

As already stated with respect to the accelerometerresults the frequencies near 600 Hz are due to themeshing of gear teeth in particular they represent thesecond-order component of the meshing frequency

Figure 8 Direct mapping of the gear system for the particle velocity for Om = 600 rmin A1 = 120 rmin and A2 = 60 rmin in thecases of (a) dry lubrication and (b) boundary lubrication

Figure 9 Comparison of the pressure velocity level spectrafor Om = 500 rmin A1 =100 rmin and A2 = 70 rmin with oil(open squares) and without oil (open circles)PVL pressure velocity level

Figure 10 Comparison of the pressure velocity level spectrafor Om = 600 rmin A1 = 120 rmin and A2 = 60 rmin with oil(open circles) and without oil (open squares)PVL pressure velocity level

Brancati et al 7

Figure 15 shows the sound level in the above fre-quency ranges for the two mean speed values of 500 rmin and 700 rmin where the effect of oil can beobserved by comparing the diagrams for the differentlubrication conditions

Gear rattle index

A gear rattle index (IGR) has been defined in previouswork and is adopted in order to compare and discrimi-nate in an objective way between different vibro-acoustic behaviours caused by different excitationsand also by different lubrication conditions The IGRwhich is referred to as the relative angular motion Du

of the gears is defined as the value of the integral714

between 20 Hz and 5000 Hz according to

IGR=

eth5000 Hz

20 Hz

Du veth THORNj j dv eth2THORN

In the present analysis the index was evaluated for theexperimental signals from the encoders for the spectrafrom the accelerometer measurements and for the spec-tra from the acoustic sound measurements

Figures 16 17 and 18 show the values of the IGRcalculated with reference to the above-mentionedexperimental measurements

It should be noted that the IGR metric gives reliableinformation with regard to the vibro-acoustic beha-viour independently of the adopted measurement meth-odology In fact the index gives qualitativelyanalogous results of the analysis performed by theencoders ie it increases with increasing A2 excitationcomponent Moreover the index includes the positiveeffect due to the oil in reducing the rattle

Conclusion

In this paper an experimental analysis of the gear rattlephenomenon was presented using a correlation between

Figure 11 Acoustic waterfall spectra versus time (dry-lubrication conditions Om = 500 rmin A1 = 100 rmin)mic microphone rpm rmin

Figure 12 Overall vibrational levelsMic microphone rpm rmin

8 Proc IMechE Part D J Automobile Engineering

Figure 13 Waterfall spectra of the acoustic signalsmic microphone rpm rmin

Figure 14 Acoustic sound level spectra for the 450ndash750 Hz rangemic microphone rpm rmin

Brancati et al 9

different measurement methodologies for the acousticsound emissions the levels of vibrations and the angu-lar motions of the gears

The study was performed on a dedicated test set-upwhere the rattle phenomenon was induced throughmulti-harmonic excitation with two components forwhich the second-order component amplitude was var-ied in particular

The acquisition of the sound pressure level fromacoustic microphones was supported by an investiga-tion with a pndashv sound intensity probe for correctevaluation of the near-field acoustic sourcesThe vibro-acoustic analysis showed notable results about thecorrelation with the encoder-based methodology whichenables an accurate analysis of the tooth contacts andimpacts occurring during the rattle to be made From

Figure 15 Sound spectra comparisons for two lubrication conditionsmic microphone rpm rmin

Figure 16 IGR for the encoder measurementsIGR gear rattle index rpm rmin

10 Proc IMechE Part D J Automobile Engineering

an acoustic viewpoint the analysis not only demon-strates that the lubricant always plays a positive role inthe reduction of the rattle noise but also shows that thepresence of the second harmonic in the excitation stillcauses an increase in the acoustic noise level In partic-ular the microphone measurements highlighted that

the second harmonic of the excitation amplifies the fre-quencies around 600 Hz (near to the second order ofgear meshing) The results of the pndashv acoustic investiga-tion instead reveal a dominant noise source in the fre-quency range 250ndash750 Hz with two dominant peakscorresponding to about 300 Hz and 600 Hz which

Figure 17 IGR for the accelerometer measurementss along the x axisIGR gear rattle index rpm rmin

Figure 18 IGR for the acoustic sound measurementsIGR gear rattle index rpm rmin

Brancati et al 11

represent the gear-meshing frequency and its second-order component respectively

The qualitative good agreement between the differ-ent methodologies was confirmed also by a perfor-mance index developed by the present authors on thebasis of the harmonic analysis of data

Although each measurement technique provides spe-cific information on the behaviour of the gears thepresent investigation makes it clear that depending onthe particular needs of the researcher it is possible toachieve similar results from a qualitative point of viewusing any one of the proposed methodologies

Acknowledgements

The authors thank Gennaro Stingo and GiuseppeIovino of the Department of Industrial EngineeringUniversity of Naples Federico II for their fundamentaltechnical support during the tuning stages of the testrig

Declaration of conflicting interests

The author(s) declared no potential conflicts of interestwith respect to the research authorship andor publi-cation of this article

Funding

The author(s) disclosed receipt of the following finan-cial support for the research authorship andor publi-cation of this article This research received no specificgrant from any funding agency in the public commer-cial or not-for-profit sectors

References

1 Wang Y Manoj R and Zhao W J Gear rattle modelingand analysis for automotive manual transmissions ProcIMechE Part D J Automobile Engineering 2001 215(2)

241ndash2582 Barthod M Hayne B Tebec JL et al Experimental study

of gear rattle excited by a multi- harmonic excitationAppl Acoust 2007 68(9) 1003ndash1025

3 Dogan S N Ryborz J and Bertsche B Design of low-noise manual automotive transmissions Proc IMechE

Part K J Multi-body Dynamics 2006 220(2) 79ndash954 Brancati R Rocca E Savino S et al Experimental analy-

sis of the relative motion of a gear pair under rattle con-ditions induced by multi-harmonic excitation In World

congress on engineering London UK 1ndash3 July 2015 pp1016ndash1021 London IAENG

5 Younes K Rigaud E Perret-Liaudet J et al Experimen-tal and numerical analysis of automotive gearbox rattlenoise J Sound Vibr 2012 331(13) 3144ndash3157

6 Brancati R Montanaro U Rocca E et al Analysis ofbifurcations rattle and chaos in a gear transmission sys-tem Int Rev Mech Engng 2013 7(4) 583ndash591

7 Rocca E and Russo R Theoretical and experimentalinvestigation into the influence of the periodic backlashfluctuations on the gear rattle J Sound Vibr 2011330(20) 4738ndash4752

8 Brancati R Rocca E and Russo R A gear rattle modelaccounting for oil squeeze between the meshing gearteeth Proc IMechE Part D J Automobile Engineering2005 219(9) 1075ndash1083

9 De la Cruz M Theodossiades S and Rahnejat H Aninvestigation of manual transmission drive rattle ProcIMechE Part K J Multi-body Dynamics 2010 224(2)167ndash181

10 Theodossiades S De la Cruz M and Rahnejat H Predic-tion of airborne radiated noise from lightly loaded lubri-cated meshing gear teeth Appl Acoust 2015 100 79ndash86

11 Brancati R Rocca E and Russo R An analysis of theautomotive driveline dynamic behaviour focusing on theinfluence of the oil squeeze effect on the idle rattle phe-nomenon J Sound Vibr 2007 303(3ndash5) 858ndash872

12 Siano D Viscardi M and Panza A Experimental acousticmeasurements in far field and near field conditions char-acterization of a beauty engine cover In 12th interna-tional conference on fluid mechanics and aerodynamics and12th international conference on heat transfer thermalengineering and environment Geneva Switzerland 29ndash31December 2014 pp 50ndash57 Geneva WSEAS

13 Siano D Viscardi M and Aiello R Experimental andnumerical validation of an automotive subsystem throughthe employment of FEMBEM approaches Energy Pro-cedia 2015 82 67ndash74

14 Brancati R Rocca E Lauria D Feasibility study of theHilbert transform in detecting the gear rattle phenom-enon of automotive transmissions Journal of Vibrationand Control prepublished February 1 2017 DOI1011771077546316689745

Appendix 1Notation

Ai amplitudes of the speed fluctuationcomponents (i = 1 2)

f fundamental frequency of the rattle cycler1 pitch radius of the pinion gearr2 pitch radius of the wheel gearz1 number of teeth on the pinion gearz2 number of teeth on the wheel gear

Du transmission errore transmission ratioui absolute rotations of the gears (i = 1 2)O angular speedOm mean value of the angular speed

12 Proc IMechE Part D J Automobile Engineering

Near-field acoustic measurements

All the acoustic measurements are evaluated in terms ofthe relative values for the different operative conditionsmore than in terms of the absolute values this consider-ation is strictly related to the characteristics of the testenvironment (semi-reverberant) which cannot beassimilated to any of the standard acoustic test environ-ments (ie anechoic semi-anechoic or reverberant)

To justify this limitation a particle velocity measure-ment technique was therefore introduced Sound-pres-sure-based measurement methods and processingtechniques often fail to provide appropriate results insuch conditions owing to the high levels of backgroundnoise Alternatively maps of the particle velocity allowthe acoustic excitations to be characterized across thesystem despite measurement in the harsh environmentMore precisely near-field experiments were performedby using novel instrumentation with the employment ofa particle velocity sensor (Microflown) TheMicroflown acoustic sensor measures the velocity12 ofair lsquoparticlesrsquo across two tiny resistive strips of platinumwhich are heated to about 300 C The temperaturechange due to a particular vibration close to the systemunder test is measured with a bridge circuit which pro-vides a signal proportional to the acoustic particle velo-city This particle velocity sensor is usually mountedtogether with a pressure microphone on a sound inten-sity pndashu probe When the particle velocity (sound) pro-pagates orthogonally across the wires it asymmetricallyalters the temperature distribution around the resistorsThe resulting resistance difference provides a broad-band (0 Hz up to at least 20 kHz) linear signal that isproportional to the particle velocity up to sound levelsof 135 dB The reliability of measuring the sound levelfrom particle velocity measurements close to rigidboundaries is well known and also in the presence ofother external sources in fact in near-field measure-ments the contributions from other directions arestrongly reduced

The measurement procedure to acquire thedata is based upon the scanning technique lsquoscan andpaintrsquo13

The displacement of the Microflown pndashu probe wasrecorded by a camera placed perpendicular to the testbench measurement area so as to avoid any visualerrors caused by the camera projection A gear rattlescan was performed by moving the sensor close to thesurface of the system The camera recorded the displa-cement of the probe using discretization with about 150points for each operating condition Each scanning ses-sion lasted about 1 min The experimental acquisitionswere processed in the frequency range 20ndash5000 Hz Theresults are combined with a background picture of themeasured environment to obtain a visual representa-tion which allows the noise source to be visualized andidentified

Figure 7 shows for Om =500 rmin A1 = 100 rmin and A2 = 70 rmin the normal particle velocityand the sound pressure maps in dry-lubrication condi-tions The velocity vector was then measured using theparticle velocity sensor and the velocity surface distri-bution in the near field can be visualized as a contourmap expressed in decibels (ie 5 310ndash8 ms) to detectlocalization of the sound sources Because the particlevelocity is a vector it is sensitive to the wave directionand the pndashu configuration provides a powerful combi-nation for suppressing extraneous noise and reflectionsduring its application

As can be seen by comparing the particle velocityand the pressure maps no sound sources external to thegears can be identified on the pressure map The reasonis that the background noise which is caused by soundsources distributed across the system is masking thedirect pressure emitted by specific areas of the vibratingstructure in contrast with the situation when viewingthe particle velocity maps It may be deduced that thegear system presents in the evaluated frequency banda most powerful excitation source which corresponds tothe gears

Figure 8(a) and (b) shows a comparison of thedirecty mapping for Om = 600 rmin A1 = 120 rminand A2 = 60 rmin in the cases of dry lubrication andboundary lubrication respectively It can be seen thatthe normal particle velocity maps for the two different

Figure 7 Direct mapping of the gear system for (a) the sound pressure and (b) the particle velocity for Om = 500 rminA1 =100 rmin and A2 =70 rmin

6 Proc IMechE Part D J Automobile Engineering

lubrication conditions highlight the positive effect oflubrication

The method to visualize and map the results in thisway represents intuitive feedback from the measure-ments allowing the noise sources across an unknownsound field to be easily localized

Figure 9 and Figure 10 show comparisons of thepressure velocity spectra with the lubricant and withoutthe lubricant respectively For Figure 9 Om = 500rmin A1 = 100 rmin and A2 =70 rmin whereas forFigure 10 Om = 600rmin A1 = 120 rmin and A2 =60 rmin The results reveal a noise source with twodominant peaks at about 300 Hz and 600 Hz whichrepresent the fundamental frequency and the second-order frequency respectively of the gear meshing Thepresence of oil reduces the noise emitted by the systemachieving about 10 dB in some frequency bands

Far-field acoustic measurements

In the present section the results of the sound pressureanalysis by employing microphones is reported Timendashfrequency graphs in the dry-lubrication conditions areshown in Figure 11 and provide evidence of the station-ary characteristics of the phenomena

An analysis of the overall levels also shows as previ-ously verified for vibrational signals an increase in theacoustic sound level as a function of the second-orderharmonic amplitude In Figure 12 the microphone over-all levels for the three mean speed values of 500 rmin600 rmin and 700 rmin for both lubrication operatingconditions are shown The far-field measurements tech-nique also reveals a sensitivity to the effect of the lubri-cant in reducing the gear rattle noise level

In Figure 13 the waterfall spectra of acoustic signalsare shown for the cases of dry lubrication and boundarylubrication respectively

From an acoustic viewpoint the frequency ranges ofmajor interest are those shown in Figure 14 iebetween 450 Hz and 750 Hz where the amplitude ofthe signals is more evident This figure shows the spec-tra of the microphone measurements for different val-ues of the average speed and different amplitudes ofthe second harmonic for dry-lubrication conditions Itcan be seen that an increase in the A2 component valuecauses an increase in the acoustic sound level

As already stated with respect to the accelerometerresults the frequencies near 600 Hz are due to themeshing of gear teeth in particular they represent thesecond-order component of the meshing frequency

Figure 8 Direct mapping of the gear system for the particle velocity for Om = 600 rmin A1 = 120 rmin and A2 = 60 rmin in thecases of (a) dry lubrication and (b) boundary lubrication

Figure 9 Comparison of the pressure velocity level spectrafor Om = 500 rmin A1 =100 rmin and A2 = 70 rmin with oil(open squares) and without oil (open circles)PVL pressure velocity level

Figure 10 Comparison of the pressure velocity level spectrafor Om = 600 rmin A1 = 120 rmin and A2 = 60 rmin with oil(open circles) and without oil (open squares)PVL pressure velocity level

Brancati et al 7

Figure 15 shows the sound level in the above fre-quency ranges for the two mean speed values of 500 rmin and 700 rmin where the effect of oil can beobserved by comparing the diagrams for the differentlubrication conditions

Gear rattle index

A gear rattle index (IGR) has been defined in previouswork and is adopted in order to compare and discrimi-nate in an objective way between different vibro-acoustic behaviours caused by different excitationsand also by different lubrication conditions The IGRwhich is referred to as the relative angular motion Du

of the gears is defined as the value of the integral714

between 20 Hz and 5000 Hz according to

IGR=

eth5000 Hz

20 Hz

Du veth THORNj j dv eth2THORN

In the present analysis the index was evaluated for theexperimental signals from the encoders for the spectrafrom the accelerometer measurements and for the spec-tra from the acoustic sound measurements

Figures 16 17 and 18 show the values of the IGRcalculated with reference to the above-mentionedexperimental measurements

It should be noted that the IGR metric gives reliableinformation with regard to the vibro-acoustic beha-viour independently of the adopted measurement meth-odology In fact the index gives qualitativelyanalogous results of the analysis performed by theencoders ie it increases with increasing A2 excitationcomponent Moreover the index includes the positiveeffect due to the oil in reducing the rattle

Conclusion

In this paper an experimental analysis of the gear rattlephenomenon was presented using a correlation between

Figure 11 Acoustic waterfall spectra versus time (dry-lubrication conditions Om = 500 rmin A1 = 100 rmin)mic microphone rpm rmin

Figure 12 Overall vibrational levelsMic microphone rpm rmin

8 Proc IMechE Part D J Automobile Engineering

Figure 13 Waterfall spectra of the acoustic signalsmic microphone rpm rmin

Figure 14 Acoustic sound level spectra for the 450ndash750 Hz rangemic microphone rpm rmin

Brancati et al 9

different measurement methodologies for the acousticsound emissions the levels of vibrations and the angu-lar motions of the gears

The study was performed on a dedicated test set-upwhere the rattle phenomenon was induced throughmulti-harmonic excitation with two components forwhich the second-order component amplitude was var-ied in particular

The acquisition of the sound pressure level fromacoustic microphones was supported by an investiga-tion with a pndashv sound intensity probe for correctevaluation of the near-field acoustic sourcesThe vibro-acoustic analysis showed notable results about thecorrelation with the encoder-based methodology whichenables an accurate analysis of the tooth contacts andimpacts occurring during the rattle to be made From

Figure 15 Sound spectra comparisons for two lubrication conditionsmic microphone rpm rmin

Figure 16 IGR for the encoder measurementsIGR gear rattle index rpm rmin

10 Proc IMechE Part D J Automobile Engineering

an acoustic viewpoint the analysis not only demon-strates that the lubricant always plays a positive role inthe reduction of the rattle noise but also shows that thepresence of the second harmonic in the excitation stillcauses an increase in the acoustic noise level In partic-ular the microphone measurements highlighted that

the second harmonic of the excitation amplifies the fre-quencies around 600 Hz (near to the second order ofgear meshing) The results of the pndashv acoustic investiga-tion instead reveal a dominant noise source in the fre-quency range 250ndash750 Hz with two dominant peakscorresponding to about 300 Hz and 600 Hz which

Figure 17 IGR for the accelerometer measurementss along the x axisIGR gear rattle index rpm rmin

Figure 18 IGR for the acoustic sound measurementsIGR gear rattle index rpm rmin

Brancati et al 11

represent the gear-meshing frequency and its second-order component respectively

The qualitative good agreement between the differ-ent methodologies was confirmed also by a perfor-mance index developed by the present authors on thebasis of the harmonic analysis of data

Although each measurement technique provides spe-cific information on the behaviour of the gears thepresent investigation makes it clear that depending onthe particular needs of the researcher it is possible toachieve similar results from a qualitative point of viewusing any one of the proposed methodologies

Acknowledgements

The authors thank Gennaro Stingo and GiuseppeIovino of the Department of Industrial EngineeringUniversity of Naples Federico II for their fundamentaltechnical support during the tuning stages of the testrig

Declaration of conflicting interests

The author(s) declared no potential conflicts of interestwith respect to the research authorship andor publi-cation of this article

Funding

The author(s) disclosed receipt of the following finan-cial support for the research authorship andor publi-cation of this article This research received no specificgrant from any funding agency in the public commer-cial or not-for-profit sectors

References

1 Wang Y Manoj R and Zhao W J Gear rattle modelingand analysis for automotive manual transmissions ProcIMechE Part D J Automobile Engineering 2001 215(2)

241ndash2582 Barthod M Hayne B Tebec JL et al Experimental study

of gear rattle excited by a multi- harmonic excitationAppl Acoust 2007 68(9) 1003ndash1025

3 Dogan S N Ryborz J and Bertsche B Design of low-noise manual automotive transmissions Proc IMechE

Part K J Multi-body Dynamics 2006 220(2) 79ndash954 Brancati R Rocca E Savino S et al Experimental analy-

sis of the relative motion of a gear pair under rattle con-ditions induced by multi-harmonic excitation In World

congress on engineering London UK 1ndash3 July 2015 pp1016ndash1021 London IAENG

5 Younes K Rigaud E Perret-Liaudet J et al Experimen-tal and numerical analysis of automotive gearbox rattlenoise J Sound Vibr 2012 331(13) 3144ndash3157

6 Brancati R Montanaro U Rocca E et al Analysis ofbifurcations rattle and chaos in a gear transmission sys-tem Int Rev Mech Engng 2013 7(4) 583ndash591

7 Rocca E and Russo R Theoretical and experimentalinvestigation into the influence of the periodic backlashfluctuations on the gear rattle J Sound Vibr 2011330(20) 4738ndash4752

8 Brancati R Rocca E and Russo R A gear rattle modelaccounting for oil squeeze between the meshing gearteeth Proc IMechE Part D J Automobile Engineering2005 219(9) 1075ndash1083

9 De la Cruz M Theodossiades S and Rahnejat H Aninvestigation of manual transmission drive rattle ProcIMechE Part K J Multi-body Dynamics 2010 224(2)167ndash181

10 Theodossiades S De la Cruz M and Rahnejat H Predic-tion of airborne radiated noise from lightly loaded lubri-cated meshing gear teeth Appl Acoust 2015 100 79ndash86

11 Brancati R Rocca E and Russo R An analysis of theautomotive driveline dynamic behaviour focusing on theinfluence of the oil squeeze effect on the idle rattle phe-nomenon J Sound Vibr 2007 303(3ndash5) 858ndash872

12 Siano D Viscardi M and Panza A Experimental acousticmeasurements in far field and near field conditions char-acterization of a beauty engine cover In 12th interna-tional conference on fluid mechanics and aerodynamics and12th international conference on heat transfer thermalengineering and environment Geneva Switzerland 29ndash31December 2014 pp 50ndash57 Geneva WSEAS

13 Siano D Viscardi M and Aiello R Experimental andnumerical validation of an automotive subsystem throughthe employment of FEMBEM approaches Energy Pro-cedia 2015 82 67ndash74

14 Brancati R Rocca E Lauria D Feasibility study of theHilbert transform in detecting the gear rattle phenom-enon of automotive transmissions Journal of Vibrationand Control prepublished February 1 2017 DOI1011771077546316689745

Appendix 1Notation

Ai amplitudes of the speed fluctuationcomponents (i = 1 2)

f fundamental frequency of the rattle cycler1 pitch radius of the pinion gearr2 pitch radius of the wheel gearz1 number of teeth on the pinion gearz2 number of teeth on the wheel gear

Du transmission errore transmission ratioui absolute rotations of the gears (i = 1 2)O angular speedOm mean value of the angular speed

12 Proc IMechE Part D J Automobile Engineering

lubrication conditions highlight the positive effect oflubrication

The method to visualize and map the results in thisway represents intuitive feedback from the measure-ments allowing the noise sources across an unknownsound field to be easily localized

Figure 9 and Figure 10 show comparisons of thepressure velocity spectra with the lubricant and withoutthe lubricant respectively For Figure 9 Om = 500rmin A1 = 100 rmin and A2 =70 rmin whereas forFigure 10 Om = 600rmin A1 = 120 rmin and A2 =60 rmin The results reveal a noise source with twodominant peaks at about 300 Hz and 600 Hz whichrepresent the fundamental frequency and the second-order frequency respectively of the gear meshing Thepresence of oil reduces the noise emitted by the systemachieving about 10 dB in some frequency bands

Far-field acoustic measurements

In the present section the results of the sound pressureanalysis by employing microphones is reported Timendashfrequency graphs in the dry-lubrication conditions areshown in Figure 11 and provide evidence of the station-ary characteristics of the phenomena

An analysis of the overall levels also shows as previ-ously verified for vibrational signals an increase in theacoustic sound level as a function of the second-orderharmonic amplitude In Figure 12 the microphone over-all levels for the three mean speed values of 500 rmin600 rmin and 700 rmin for both lubrication operatingconditions are shown The far-field measurements tech-nique also reveals a sensitivity to the effect of the lubri-cant in reducing the gear rattle noise level

In Figure 13 the waterfall spectra of acoustic signalsare shown for the cases of dry lubrication and boundarylubrication respectively

From an acoustic viewpoint the frequency ranges ofmajor interest are those shown in Figure 14 iebetween 450 Hz and 750 Hz where the amplitude ofthe signals is more evident This figure shows the spec-tra of the microphone measurements for different val-ues of the average speed and different amplitudes ofthe second harmonic for dry-lubrication conditions Itcan be seen that an increase in the A2 component valuecauses an increase in the acoustic sound level

As already stated with respect to the accelerometerresults the frequencies near 600 Hz are due to themeshing of gear teeth in particular they represent thesecond-order component of the meshing frequency

Figure 8 Direct mapping of the gear system for the particle velocity for Om = 600 rmin A1 = 120 rmin and A2 = 60 rmin in thecases of (a) dry lubrication and (b) boundary lubrication

Figure 9 Comparison of the pressure velocity level spectrafor Om = 500 rmin A1 =100 rmin and A2 = 70 rmin with oil(open squares) and without oil (open circles)PVL pressure velocity level

Figure 10 Comparison of the pressure velocity level spectrafor Om = 600 rmin A1 = 120 rmin and A2 = 60 rmin with oil(open circles) and without oil (open squares)PVL pressure velocity level

Brancati et al 7

Figure 15 shows the sound level in the above fre-quency ranges for the two mean speed values of 500 rmin and 700 rmin where the effect of oil can beobserved by comparing the diagrams for the differentlubrication conditions

Gear rattle index

A gear rattle index (IGR) has been defined in previouswork and is adopted in order to compare and discrimi-nate in an objective way between different vibro-acoustic behaviours caused by different excitationsand also by different lubrication conditions The IGRwhich is referred to as the relative angular motion Du

of the gears is defined as the value of the integral714

between 20 Hz and 5000 Hz according to

IGR=

eth5000 Hz

20 Hz

Du veth THORNj j dv eth2THORN

In the present analysis the index was evaluated for theexperimental signals from the encoders for the spectrafrom the accelerometer measurements and for the spec-tra from the acoustic sound measurements

Figures 16 17 and 18 show the values of the IGRcalculated with reference to the above-mentionedexperimental measurements

It should be noted that the IGR metric gives reliableinformation with regard to the vibro-acoustic beha-viour independently of the adopted measurement meth-odology In fact the index gives qualitativelyanalogous results of the analysis performed by theencoders ie it increases with increasing A2 excitationcomponent Moreover the index includes the positiveeffect due to the oil in reducing the rattle

Conclusion

In this paper an experimental analysis of the gear rattlephenomenon was presented using a correlation between

Figure 11 Acoustic waterfall spectra versus time (dry-lubrication conditions Om = 500 rmin A1 = 100 rmin)mic microphone rpm rmin

Figure 12 Overall vibrational levelsMic microphone rpm rmin

8 Proc IMechE Part D J Automobile Engineering

Figure 13 Waterfall spectra of the acoustic signalsmic microphone rpm rmin

Figure 14 Acoustic sound level spectra for the 450ndash750 Hz rangemic microphone rpm rmin

Brancati et al 9

different measurement methodologies for the acousticsound emissions the levels of vibrations and the angu-lar motions of the gears

The study was performed on a dedicated test set-upwhere the rattle phenomenon was induced throughmulti-harmonic excitation with two components forwhich the second-order component amplitude was var-ied in particular

The acquisition of the sound pressure level fromacoustic microphones was supported by an investiga-tion with a pndashv sound intensity probe for correctevaluation of the near-field acoustic sourcesThe vibro-acoustic analysis showed notable results about thecorrelation with the encoder-based methodology whichenables an accurate analysis of the tooth contacts andimpacts occurring during the rattle to be made From

Figure 15 Sound spectra comparisons for two lubrication conditionsmic microphone rpm rmin

Figure 16 IGR for the encoder measurementsIGR gear rattle index rpm rmin

10 Proc IMechE Part D J Automobile Engineering

an acoustic viewpoint the analysis not only demon-strates that the lubricant always plays a positive role inthe reduction of the rattle noise but also shows that thepresence of the second harmonic in the excitation stillcauses an increase in the acoustic noise level In partic-ular the microphone measurements highlighted that

the second harmonic of the excitation amplifies the fre-quencies around 600 Hz (near to the second order ofgear meshing) The results of the pndashv acoustic investiga-tion instead reveal a dominant noise source in the fre-quency range 250ndash750 Hz with two dominant peakscorresponding to about 300 Hz and 600 Hz which

Figure 17 IGR for the accelerometer measurementss along the x axisIGR gear rattle index rpm rmin

Figure 18 IGR for the acoustic sound measurementsIGR gear rattle index rpm rmin

Brancati et al 11

represent the gear-meshing frequency and its second-order component respectively

The qualitative good agreement between the differ-ent methodologies was confirmed also by a perfor-mance index developed by the present authors on thebasis of the harmonic analysis of data

Although each measurement technique provides spe-cific information on the behaviour of the gears thepresent investigation makes it clear that depending onthe particular needs of the researcher it is possible toachieve similar results from a qualitative point of viewusing any one of the proposed methodologies

Acknowledgements

The authors thank Gennaro Stingo and GiuseppeIovino of the Department of Industrial EngineeringUniversity of Naples Federico II for their fundamentaltechnical support during the tuning stages of the testrig

Declaration of conflicting interests

The author(s) declared no potential conflicts of interestwith respect to the research authorship andor publi-cation of this article

Funding

The author(s) disclosed receipt of the following finan-cial support for the research authorship andor publi-cation of this article This research received no specificgrant from any funding agency in the public commer-cial or not-for-profit sectors

References

1 Wang Y Manoj R and Zhao W J Gear rattle modelingand analysis for automotive manual transmissions ProcIMechE Part D J Automobile Engineering 2001 215(2)

241ndash2582 Barthod M Hayne B Tebec JL et al Experimental study

of gear rattle excited by a multi- harmonic excitationAppl Acoust 2007 68(9) 1003ndash1025

3 Dogan S N Ryborz J and Bertsche B Design of low-noise manual automotive transmissions Proc IMechE

Part K J Multi-body Dynamics 2006 220(2) 79ndash954 Brancati R Rocca E Savino S et al Experimental analy-

sis of the relative motion of a gear pair under rattle con-ditions induced by multi-harmonic excitation In World

congress on engineering London UK 1ndash3 July 2015 pp1016ndash1021 London IAENG

5 Younes K Rigaud E Perret-Liaudet J et al Experimen-tal and numerical analysis of automotive gearbox rattlenoise J Sound Vibr 2012 331(13) 3144ndash3157

6 Brancati R Montanaro U Rocca E et al Analysis ofbifurcations rattle and chaos in a gear transmission sys-tem Int Rev Mech Engng 2013 7(4) 583ndash591

7 Rocca E and Russo R Theoretical and experimentalinvestigation into the influence of the periodic backlashfluctuations on the gear rattle J Sound Vibr 2011330(20) 4738ndash4752

8 Brancati R Rocca E and Russo R A gear rattle modelaccounting for oil squeeze between the meshing gearteeth Proc IMechE Part D J Automobile Engineering2005 219(9) 1075ndash1083

9 De la Cruz M Theodossiades S and Rahnejat H Aninvestigation of manual transmission drive rattle ProcIMechE Part K J Multi-body Dynamics 2010 224(2)167ndash181

10 Theodossiades S De la Cruz M and Rahnejat H Predic-tion of airborne radiated noise from lightly loaded lubri-cated meshing gear teeth Appl Acoust 2015 100 79ndash86

11 Brancati R Rocca E and Russo R An analysis of theautomotive driveline dynamic behaviour focusing on theinfluence of the oil squeeze effect on the idle rattle phe-nomenon J Sound Vibr 2007 303(3ndash5) 858ndash872

12 Siano D Viscardi M and Panza A Experimental acousticmeasurements in far field and near field conditions char-acterization of a beauty engine cover In 12th interna-tional conference on fluid mechanics and aerodynamics and12th international conference on heat transfer thermalengineering and environment Geneva Switzerland 29ndash31December 2014 pp 50ndash57 Geneva WSEAS

13 Siano D Viscardi M and Aiello R Experimental andnumerical validation of an automotive subsystem throughthe employment of FEMBEM approaches Energy Pro-cedia 2015 82 67ndash74

14 Brancati R Rocca E Lauria D Feasibility study of theHilbert transform in detecting the gear rattle phenom-enon of automotive transmissions Journal of Vibrationand Control prepublished February 1 2017 DOI1011771077546316689745

Appendix 1Notation

Ai amplitudes of the speed fluctuationcomponents (i = 1 2)

f fundamental frequency of the rattle cycler1 pitch radius of the pinion gearr2 pitch radius of the wheel gearz1 number of teeth on the pinion gearz2 number of teeth on the wheel gear

Du transmission errore transmission ratioui absolute rotations of the gears (i = 1 2)O angular speedOm mean value of the angular speed

12 Proc IMechE Part D J Automobile Engineering

Figure 15 shows the sound level in the above fre-quency ranges for the two mean speed values of 500 rmin and 700 rmin where the effect of oil can beobserved by comparing the diagrams for the differentlubrication conditions

Gear rattle index

A gear rattle index (IGR) has been defined in previouswork and is adopted in order to compare and discrimi-nate in an objective way between different vibro-acoustic behaviours caused by different excitationsand also by different lubrication conditions The IGRwhich is referred to as the relative angular motion Du

of the gears is defined as the value of the integral714

between 20 Hz and 5000 Hz according to

IGR=

eth5000 Hz

20 Hz

Du veth THORNj j dv eth2THORN

In the present analysis the index was evaluated for theexperimental signals from the encoders for the spectrafrom the accelerometer measurements and for the spec-tra from the acoustic sound measurements

Figures 16 17 and 18 show the values of the IGRcalculated with reference to the above-mentionedexperimental measurements

It should be noted that the IGR metric gives reliableinformation with regard to the vibro-acoustic beha-viour independently of the adopted measurement meth-odology In fact the index gives qualitativelyanalogous results of the analysis performed by theencoders ie it increases with increasing A2 excitationcomponent Moreover the index includes the positiveeffect due to the oil in reducing the rattle

Conclusion

In this paper an experimental analysis of the gear rattlephenomenon was presented using a correlation between

Figure 11 Acoustic waterfall spectra versus time (dry-lubrication conditions Om = 500 rmin A1 = 100 rmin)mic microphone rpm rmin

Figure 12 Overall vibrational levelsMic microphone rpm rmin

8 Proc IMechE Part D J Automobile Engineering

Figure 13 Waterfall spectra of the acoustic signalsmic microphone rpm rmin

Figure 14 Acoustic sound level spectra for the 450ndash750 Hz rangemic microphone rpm rmin

Brancati et al 9

different measurement methodologies for the acousticsound emissions the levels of vibrations and the angu-lar motions of the gears

The study was performed on a dedicated test set-upwhere the rattle phenomenon was induced throughmulti-harmonic excitation with two components forwhich the second-order component amplitude was var-ied in particular

The acquisition of the sound pressure level fromacoustic microphones was supported by an investiga-tion with a pndashv sound intensity probe for correctevaluation of the near-field acoustic sourcesThe vibro-acoustic analysis showed notable results about thecorrelation with the encoder-based methodology whichenables an accurate analysis of the tooth contacts andimpacts occurring during the rattle to be made From

Figure 15 Sound spectra comparisons for two lubrication conditionsmic microphone rpm rmin

Figure 16 IGR for the encoder measurementsIGR gear rattle index rpm rmin

10 Proc IMechE Part D J Automobile Engineering

an acoustic viewpoint the analysis not only demon-strates that the lubricant always plays a positive role inthe reduction of the rattle noise but also shows that thepresence of the second harmonic in the excitation stillcauses an increase in the acoustic noise level In partic-ular the microphone measurements highlighted that

the second harmonic of the excitation amplifies the fre-quencies around 600 Hz (near to the second order ofgear meshing) The results of the pndashv acoustic investiga-tion instead reveal a dominant noise source in the fre-quency range 250ndash750 Hz with two dominant peakscorresponding to about 300 Hz and 600 Hz which

Figure 17 IGR for the accelerometer measurementss along the x axisIGR gear rattle index rpm rmin

Figure 18 IGR for the acoustic sound measurementsIGR gear rattle index rpm rmin

Brancati et al 11

represent the gear-meshing frequency and its second-order component respectively

The qualitative good agreement between the differ-ent methodologies was confirmed also by a perfor-mance index developed by the present authors on thebasis of the harmonic analysis of data

Although each measurement technique provides spe-cific information on the behaviour of the gears thepresent investigation makes it clear that depending onthe particular needs of the researcher it is possible toachieve similar results from a qualitative point of viewusing any one of the proposed methodologies

Acknowledgements

The authors thank Gennaro Stingo and GiuseppeIovino of the Department of Industrial EngineeringUniversity of Naples Federico II for their fundamentaltechnical support during the tuning stages of the testrig

Declaration of conflicting interests

The author(s) declared no potential conflicts of interestwith respect to the research authorship andor publi-cation of this article

Funding

The author(s) disclosed receipt of the following finan-cial support for the research authorship andor publi-cation of this article This research received no specificgrant from any funding agency in the public commer-cial or not-for-profit sectors

References

1 Wang Y Manoj R and Zhao W J Gear rattle modelingand analysis for automotive manual transmissions ProcIMechE Part D J Automobile Engineering 2001 215(2)

241ndash2582 Barthod M Hayne B Tebec JL et al Experimental study

of gear rattle excited by a multi- harmonic excitationAppl Acoust 2007 68(9) 1003ndash1025

3 Dogan S N Ryborz J and Bertsche B Design of low-noise manual automotive transmissions Proc IMechE

Part K J Multi-body Dynamics 2006 220(2) 79ndash954 Brancati R Rocca E Savino S et al Experimental analy-

sis of the relative motion of a gear pair under rattle con-ditions induced by multi-harmonic excitation In World

congress on engineering London UK 1ndash3 July 2015 pp1016ndash1021 London IAENG

5 Younes K Rigaud E Perret-Liaudet J et al Experimen-tal and numerical analysis of automotive gearbox rattlenoise J Sound Vibr 2012 331(13) 3144ndash3157

6 Brancati R Montanaro U Rocca E et al Analysis ofbifurcations rattle and chaos in a gear transmission sys-tem Int Rev Mech Engng 2013 7(4) 583ndash591

7 Rocca E and Russo R Theoretical and experimentalinvestigation into the influence of the periodic backlashfluctuations on the gear rattle J Sound Vibr 2011330(20) 4738ndash4752

8 Brancati R Rocca E and Russo R A gear rattle modelaccounting for oil squeeze between the meshing gearteeth Proc IMechE Part D J Automobile Engineering2005 219(9) 1075ndash1083

9 De la Cruz M Theodossiades S and Rahnejat H Aninvestigation of manual transmission drive rattle ProcIMechE Part K J Multi-body Dynamics 2010 224(2)167ndash181

10 Theodossiades S De la Cruz M and Rahnejat H Predic-tion of airborne radiated noise from lightly loaded lubri-cated meshing gear teeth Appl Acoust 2015 100 79ndash86

11 Brancati R Rocca E and Russo R An analysis of theautomotive driveline dynamic behaviour focusing on theinfluence of the oil squeeze effect on the idle rattle phe-nomenon J Sound Vibr 2007 303(3ndash5) 858ndash872

12 Siano D Viscardi M and Panza A Experimental acousticmeasurements in far field and near field conditions char-acterization of a beauty engine cover In 12th interna-tional conference on fluid mechanics and aerodynamics and12th international conference on heat transfer thermalengineering and environment Geneva Switzerland 29ndash31December 2014 pp 50ndash57 Geneva WSEAS

13 Siano D Viscardi M and Aiello R Experimental andnumerical validation of an automotive subsystem throughthe employment of FEMBEM approaches Energy Pro-cedia 2015 82 67ndash74

14 Brancati R Rocca E Lauria D Feasibility study of theHilbert transform in detecting the gear rattle phenom-enon of automotive transmissions Journal of Vibrationand Control prepublished February 1 2017 DOI1011771077546316689745

Appendix 1Notation

Ai amplitudes of the speed fluctuationcomponents (i = 1 2)

f fundamental frequency of the rattle cycler1 pitch radius of the pinion gearr2 pitch radius of the wheel gearz1 number of teeth on the pinion gearz2 number of teeth on the wheel gear

Du transmission errore transmission ratioui absolute rotations of the gears (i = 1 2)O angular speedOm mean value of the angular speed

12 Proc IMechE Part D J Automobile Engineering

Figure 13 Waterfall spectra of the acoustic signalsmic microphone rpm rmin

Figure 14 Acoustic sound level spectra for the 450ndash750 Hz rangemic microphone rpm rmin

Brancati et al 9

different measurement methodologies for the acousticsound emissions the levels of vibrations and the angu-lar motions of the gears

The study was performed on a dedicated test set-upwhere the rattle phenomenon was induced throughmulti-harmonic excitation with two components forwhich the second-order component amplitude was var-ied in particular

The acquisition of the sound pressure level fromacoustic microphones was supported by an investiga-tion with a pndashv sound intensity probe for correctevaluation of the near-field acoustic sourcesThe vibro-acoustic analysis showed notable results about thecorrelation with the encoder-based methodology whichenables an accurate analysis of the tooth contacts andimpacts occurring during the rattle to be made From

Figure 15 Sound spectra comparisons for two lubrication conditionsmic microphone rpm rmin

Figure 16 IGR for the encoder measurementsIGR gear rattle index rpm rmin

10 Proc IMechE Part D J Automobile Engineering

an acoustic viewpoint the analysis not only demon-strates that the lubricant always plays a positive role inthe reduction of the rattle noise but also shows that thepresence of the second harmonic in the excitation stillcauses an increase in the acoustic noise level In partic-ular the microphone measurements highlighted that

the second harmonic of the excitation amplifies the fre-quencies around 600 Hz (near to the second order ofgear meshing) The results of the pndashv acoustic investiga-tion instead reveal a dominant noise source in the fre-quency range 250ndash750 Hz with two dominant peakscorresponding to about 300 Hz and 600 Hz which

Figure 17 IGR for the accelerometer measurementss along the x axisIGR gear rattle index rpm rmin

Figure 18 IGR for the acoustic sound measurementsIGR gear rattle index rpm rmin

Brancati et al 11

represent the gear-meshing frequency and its second-order component respectively

The qualitative good agreement between the differ-ent methodologies was confirmed also by a perfor-mance index developed by the present authors on thebasis of the harmonic analysis of data

Although each measurement technique provides spe-cific information on the behaviour of the gears thepresent investigation makes it clear that depending onthe particular needs of the researcher it is possible toachieve similar results from a qualitative point of viewusing any one of the proposed methodologies

Acknowledgements

The authors thank Gennaro Stingo and GiuseppeIovino of the Department of Industrial EngineeringUniversity of Naples Federico II for their fundamentaltechnical support during the tuning stages of the testrig

Declaration of conflicting interests

The author(s) declared no potential conflicts of interestwith respect to the research authorship andor publi-cation of this article

Funding

The author(s) disclosed receipt of the following finan-cial support for the research authorship andor publi-cation of this article This research received no specificgrant from any funding agency in the public commer-cial or not-for-profit sectors

References

1 Wang Y Manoj R and Zhao W J Gear rattle modelingand analysis for automotive manual transmissions ProcIMechE Part D J Automobile Engineering 2001 215(2)

241ndash2582 Barthod M Hayne B Tebec JL et al Experimental study

of gear rattle excited by a multi- harmonic excitationAppl Acoust 2007 68(9) 1003ndash1025

3 Dogan S N Ryborz J and Bertsche B Design of low-noise manual automotive transmissions Proc IMechE

Part K J Multi-body Dynamics 2006 220(2) 79ndash954 Brancati R Rocca E Savino S et al Experimental analy-

sis of the relative motion of a gear pair under rattle con-ditions induced by multi-harmonic excitation In World

congress on engineering London UK 1ndash3 July 2015 pp1016ndash1021 London IAENG

5 Younes K Rigaud E Perret-Liaudet J et al Experimen-tal and numerical analysis of automotive gearbox rattlenoise J Sound Vibr 2012 331(13) 3144ndash3157

6 Brancati R Montanaro U Rocca E et al Analysis ofbifurcations rattle and chaos in a gear transmission sys-tem Int Rev Mech Engng 2013 7(4) 583ndash591

7 Rocca E and Russo R Theoretical and experimentalinvestigation into the influence of the periodic backlashfluctuations on the gear rattle J Sound Vibr 2011330(20) 4738ndash4752

8 Brancati R Rocca E and Russo R A gear rattle modelaccounting for oil squeeze between the meshing gearteeth Proc IMechE Part D J Automobile Engineering2005 219(9) 1075ndash1083

9 De la Cruz M Theodossiades S and Rahnejat H Aninvestigation of manual transmission drive rattle ProcIMechE Part K J Multi-body Dynamics 2010 224(2)167ndash181

10 Theodossiades S De la Cruz M and Rahnejat H Predic-tion of airborne radiated noise from lightly loaded lubri-cated meshing gear teeth Appl Acoust 2015 100 79ndash86

11 Brancati R Rocca E and Russo R An analysis of theautomotive driveline dynamic behaviour focusing on theinfluence of the oil squeeze effect on the idle rattle phe-nomenon J Sound Vibr 2007 303(3ndash5) 858ndash872

12 Siano D Viscardi M and Panza A Experimental acousticmeasurements in far field and near field conditions char-acterization of a beauty engine cover In 12th interna-tional conference on fluid mechanics and aerodynamics and12th international conference on heat transfer thermalengineering and environment Geneva Switzerland 29ndash31December 2014 pp 50ndash57 Geneva WSEAS

13 Siano D Viscardi M and Aiello R Experimental andnumerical validation of an automotive subsystem throughthe employment of FEMBEM approaches Energy Pro-cedia 2015 82 67ndash74

14 Brancati R Rocca E Lauria D Feasibility study of theHilbert transform in detecting the gear rattle phenom-enon of automotive transmissions Journal of Vibrationand Control prepublished February 1 2017 DOI1011771077546316689745

Appendix 1Notation

Ai amplitudes of the speed fluctuationcomponents (i = 1 2)

f fundamental frequency of the rattle cycler1 pitch radius of the pinion gearr2 pitch radius of the wheel gearz1 number of teeth on the pinion gearz2 number of teeth on the wheel gear

Du transmission errore transmission ratioui absolute rotations of the gears (i = 1 2)O angular speedOm mean value of the angular speed

12 Proc IMechE Part D J Automobile Engineering

different measurement methodologies for the acousticsound emissions the levels of vibrations and the angu-lar motions of the gears

The study was performed on a dedicated test set-upwhere the rattle phenomenon was induced throughmulti-harmonic excitation with two components forwhich the second-order component amplitude was var-ied in particular

The acquisition of the sound pressure level fromacoustic microphones was supported by an investiga-tion with a pndashv sound intensity probe for correctevaluation of the near-field acoustic sourcesThe vibro-acoustic analysis showed notable results about thecorrelation with the encoder-based methodology whichenables an accurate analysis of the tooth contacts andimpacts occurring during the rattle to be made From

Figure 15 Sound spectra comparisons for two lubrication conditionsmic microphone rpm rmin

Figure 16 IGR for the encoder measurementsIGR gear rattle index rpm rmin

10 Proc IMechE Part D J Automobile Engineering

an acoustic viewpoint the analysis not only demon-strates that the lubricant always plays a positive role inthe reduction of the rattle noise but also shows that thepresence of the second harmonic in the excitation stillcauses an increase in the acoustic noise level In partic-ular the microphone measurements highlighted that

the second harmonic of the excitation amplifies the fre-quencies around 600 Hz (near to the second order ofgear meshing) The results of the pndashv acoustic investiga-tion instead reveal a dominant noise source in the fre-quency range 250ndash750 Hz with two dominant peakscorresponding to about 300 Hz and 600 Hz which

Figure 17 IGR for the accelerometer measurementss along the x axisIGR gear rattle index rpm rmin

Figure 18 IGR for the acoustic sound measurementsIGR gear rattle index rpm rmin

Brancati et al 11

represent the gear-meshing frequency and its second-order component respectively

The qualitative good agreement between the differ-ent methodologies was confirmed also by a perfor-mance index developed by the present authors on thebasis of the harmonic analysis of data

Although each measurement technique provides spe-cific information on the behaviour of the gears thepresent investigation makes it clear that depending onthe particular needs of the researcher it is possible toachieve similar results from a qualitative point of viewusing any one of the proposed methodologies

Acknowledgements

The authors thank Gennaro Stingo and GiuseppeIovino of the Department of Industrial EngineeringUniversity of Naples Federico II for their fundamentaltechnical support during the tuning stages of the testrig

Declaration of conflicting interests

The author(s) declared no potential conflicts of interestwith respect to the research authorship andor publi-cation of this article

Funding

The author(s) disclosed receipt of the following finan-cial support for the research authorship andor publi-cation of this article This research received no specificgrant from any funding agency in the public commer-cial or not-for-profit sectors

References

1 Wang Y Manoj R and Zhao W J Gear rattle modelingand analysis for automotive manual transmissions ProcIMechE Part D J Automobile Engineering 2001 215(2)

241ndash2582 Barthod M Hayne B Tebec JL et al Experimental study

of gear rattle excited by a multi- harmonic excitationAppl Acoust 2007 68(9) 1003ndash1025

3 Dogan S N Ryborz J and Bertsche B Design of low-noise manual automotive transmissions Proc IMechE

Part K J Multi-body Dynamics 2006 220(2) 79ndash954 Brancati R Rocca E Savino S et al Experimental analy-

sis of the relative motion of a gear pair under rattle con-ditions induced by multi-harmonic excitation In World

congress on engineering London UK 1ndash3 July 2015 pp1016ndash1021 London IAENG

5 Younes K Rigaud E Perret-Liaudet J et al Experimen-tal and numerical analysis of automotive gearbox rattlenoise J Sound Vibr 2012 331(13) 3144ndash3157

6 Brancati R Montanaro U Rocca E et al Analysis ofbifurcations rattle and chaos in a gear transmission sys-tem Int Rev Mech Engng 2013 7(4) 583ndash591

7 Rocca E and Russo R Theoretical and experimentalinvestigation into the influence of the periodic backlashfluctuations on the gear rattle J Sound Vibr 2011330(20) 4738ndash4752

8 Brancati R Rocca E and Russo R A gear rattle modelaccounting for oil squeeze between the meshing gearteeth Proc IMechE Part D J Automobile Engineering2005 219(9) 1075ndash1083

9 De la Cruz M Theodossiades S and Rahnejat H Aninvestigation of manual transmission drive rattle ProcIMechE Part K J Multi-body Dynamics 2010 224(2)167ndash181

10 Theodossiades S De la Cruz M and Rahnejat H Predic-tion of airborne radiated noise from lightly loaded lubri-cated meshing gear teeth Appl Acoust 2015 100 79ndash86

11 Brancati R Rocca E and Russo R An analysis of theautomotive driveline dynamic behaviour focusing on theinfluence of the oil squeeze effect on the idle rattle phe-nomenon J Sound Vibr 2007 303(3ndash5) 858ndash872

12 Siano D Viscardi M and Panza A Experimental acousticmeasurements in far field and near field conditions char-acterization of a beauty engine cover In 12th interna-tional conference on fluid mechanics and aerodynamics and12th international conference on heat transfer thermalengineering and environment Geneva Switzerland 29ndash31December 2014 pp 50ndash57 Geneva WSEAS

13 Siano D Viscardi M and Aiello R Experimental andnumerical validation of an automotive subsystem throughthe employment of FEMBEM approaches Energy Pro-cedia 2015 82 67ndash74

14 Brancati R Rocca E Lauria D Feasibility study of theHilbert transform in detecting the gear rattle phenom-enon of automotive transmissions Journal of Vibrationand Control prepublished February 1 2017 DOI1011771077546316689745

Appendix 1Notation

Ai amplitudes of the speed fluctuationcomponents (i = 1 2)

f fundamental frequency of the rattle cycler1 pitch radius of the pinion gearr2 pitch radius of the wheel gearz1 number of teeth on the pinion gearz2 number of teeth on the wheel gear

Du transmission errore transmission ratioui absolute rotations of the gears (i = 1 2)O angular speedOm mean value of the angular speed

12 Proc IMechE Part D J Automobile Engineering

an acoustic viewpoint the analysis not only demon-strates that the lubricant always plays a positive role inthe reduction of the rattle noise but also shows that thepresence of the second harmonic in the excitation stillcauses an increase in the acoustic noise level In partic-ular the microphone measurements highlighted that

the second harmonic of the excitation amplifies the fre-quencies around 600 Hz (near to the second order ofgear meshing) The results of the pndashv acoustic investiga-tion instead reveal a dominant noise source in the fre-quency range 250ndash750 Hz with two dominant peakscorresponding to about 300 Hz and 600 Hz which

Figure 17 IGR for the accelerometer measurementss along the x axisIGR gear rattle index rpm rmin

Figure 18 IGR for the acoustic sound measurementsIGR gear rattle index rpm rmin

Brancati et al 11

represent the gear-meshing frequency and its second-order component respectively

The qualitative good agreement between the differ-ent methodologies was confirmed also by a perfor-mance index developed by the present authors on thebasis of the harmonic analysis of data

Although each measurement technique provides spe-cific information on the behaviour of the gears thepresent investigation makes it clear that depending onthe particular needs of the researcher it is possible toachieve similar results from a qualitative point of viewusing any one of the proposed methodologies

Acknowledgements

The authors thank Gennaro Stingo and GiuseppeIovino of the Department of Industrial EngineeringUniversity of Naples Federico II for their fundamentaltechnical support during the tuning stages of the testrig

Declaration of conflicting interests

The author(s) declared no potential conflicts of interestwith respect to the research authorship andor publi-cation of this article

Funding

The author(s) disclosed receipt of the following finan-cial support for the research authorship andor publi-cation of this article This research received no specificgrant from any funding agency in the public commer-cial or not-for-profit sectors

References

1 Wang Y Manoj R and Zhao W J Gear rattle modelingand analysis for automotive manual transmissions ProcIMechE Part D J Automobile Engineering 2001 215(2)

241ndash2582 Barthod M Hayne B Tebec JL et al Experimental study

of gear rattle excited by a multi- harmonic excitationAppl Acoust 2007 68(9) 1003ndash1025

3 Dogan S N Ryborz J and Bertsche B Design of low-noise manual automotive transmissions Proc IMechE

Part K J Multi-body Dynamics 2006 220(2) 79ndash954 Brancati R Rocca E Savino S et al Experimental analy-

sis of the relative motion of a gear pair under rattle con-ditions induced by multi-harmonic excitation In World

congress on engineering London UK 1ndash3 July 2015 pp1016ndash1021 London IAENG

5 Younes K Rigaud E Perret-Liaudet J et al Experimen-tal and numerical analysis of automotive gearbox rattlenoise J Sound Vibr 2012 331(13) 3144ndash3157

6 Brancati R Montanaro U Rocca E et al Analysis ofbifurcations rattle and chaos in a gear transmission sys-tem Int Rev Mech Engng 2013 7(4) 583ndash591

7 Rocca E and Russo R Theoretical and experimentalinvestigation into the influence of the periodic backlashfluctuations on the gear rattle J Sound Vibr 2011330(20) 4738ndash4752

8 Brancati R Rocca E and Russo R A gear rattle modelaccounting for oil squeeze between the meshing gearteeth Proc IMechE Part D J Automobile Engineering2005 219(9) 1075ndash1083

9 De la Cruz M Theodossiades S and Rahnejat H Aninvestigation of manual transmission drive rattle ProcIMechE Part K J Multi-body Dynamics 2010 224(2)167ndash181

10 Theodossiades S De la Cruz M and Rahnejat H Predic-tion of airborne radiated noise from lightly loaded lubri-cated meshing gear teeth Appl Acoust 2015 100 79ndash86

11 Brancati R Rocca E and Russo R An analysis of theautomotive driveline dynamic behaviour focusing on theinfluence of the oil squeeze effect on the idle rattle phe-nomenon J Sound Vibr 2007 303(3ndash5) 858ndash872

12 Siano D Viscardi M and Panza A Experimental acousticmeasurements in far field and near field conditions char-acterization of a beauty engine cover In 12th interna-tional conference on fluid mechanics and aerodynamics and12th international conference on heat transfer thermalengineering and environment Geneva Switzerland 29ndash31December 2014 pp 50ndash57 Geneva WSEAS

13 Siano D Viscardi M and Aiello R Experimental andnumerical validation of an automotive subsystem throughthe employment of FEMBEM approaches Energy Pro-cedia 2015 82 67ndash74

14 Brancati R Rocca E Lauria D Feasibility study of theHilbert transform in detecting the gear rattle phenom-enon of automotive transmissions Journal of Vibrationand Control prepublished February 1 2017 DOI1011771077546316689745

Appendix 1Notation

Ai amplitudes of the speed fluctuationcomponents (i = 1 2)

f fundamental frequency of the rattle cycler1 pitch radius of the pinion gearr2 pitch radius of the wheel gearz1 number of teeth on the pinion gearz2 number of teeth on the wheel gear

Du transmission errore transmission ratioui absolute rotations of the gears (i = 1 2)O angular speedOm mean value of the angular speed

12 Proc IMechE Part D J Automobile Engineering

represent the gear-meshing frequency and its second-order component respectively

The qualitative good agreement between the differ-ent methodologies was confirmed also by a perfor-mance index developed by the present authors on thebasis of the harmonic analysis of data

Although each measurement technique provides spe-cific information on the behaviour of the gears thepresent investigation makes it clear that depending onthe particular needs of the researcher it is possible toachieve similar results from a qualitative point of viewusing any one of the proposed methodologies

Acknowledgements

The authors thank Gennaro Stingo and GiuseppeIovino of the Department of Industrial EngineeringUniversity of Naples Federico II for their fundamentaltechnical support during the tuning stages of the testrig

Declaration of conflicting interests

The author(s) declared no potential conflicts of interestwith respect to the research authorship andor publi-cation of this article

Funding

The author(s) disclosed receipt of the following finan-cial support for the research authorship andor publi-cation of this article This research received no specificgrant from any funding agency in the public commer-cial or not-for-profit sectors

References

1 Wang Y Manoj R and Zhao W J Gear rattle modelingand analysis for automotive manual transmissions ProcIMechE Part D J Automobile Engineering 2001 215(2)

241ndash2582 Barthod M Hayne B Tebec JL et al Experimental study

of gear rattle excited by a multi- harmonic excitationAppl Acoust 2007 68(9) 1003ndash1025

3 Dogan S N Ryborz J and Bertsche B Design of low-noise manual automotive transmissions Proc IMechE

Part K J Multi-body Dynamics 2006 220(2) 79ndash954 Brancati R Rocca E Savino S et al Experimental analy-

sis of the relative motion of a gear pair under rattle con-ditions induced by multi-harmonic excitation In World

congress on engineering London UK 1ndash3 July 2015 pp1016ndash1021 London IAENG

5 Younes K Rigaud E Perret-Liaudet J et al Experimen-tal and numerical analysis of automotive gearbox rattlenoise J Sound Vibr 2012 331(13) 3144ndash3157

6 Brancati R Montanaro U Rocca E et al Analysis ofbifurcations rattle and chaos in a gear transmission sys-tem Int Rev Mech Engng 2013 7(4) 583ndash591

7 Rocca E and Russo R Theoretical and experimentalinvestigation into the influence of the periodic backlashfluctuations on the gear rattle J Sound Vibr 2011330(20) 4738ndash4752

8 Brancati R Rocca E and Russo R A gear rattle modelaccounting for oil squeeze between the meshing gearteeth Proc IMechE Part D J Automobile Engineering2005 219(9) 1075ndash1083

9 De la Cruz M Theodossiades S and Rahnejat H Aninvestigation of manual transmission drive rattle ProcIMechE Part K J Multi-body Dynamics 2010 224(2)167ndash181

10 Theodossiades S De la Cruz M and Rahnejat H Predic-tion of airborne radiated noise from lightly loaded lubri-cated meshing gear teeth Appl Acoust 2015 100 79ndash86

11 Brancati R Rocca E and Russo R An analysis of theautomotive driveline dynamic behaviour focusing on theinfluence of the oil squeeze effect on the idle rattle phe-nomenon J Sound Vibr 2007 303(3ndash5) 858ndash872

12 Siano D Viscardi M and Panza A Experimental acousticmeasurements in far field and near field conditions char-acterization of a beauty engine cover In 12th interna-tional conference on fluid mechanics and aerodynamics and12th international conference on heat transfer thermalengineering and environment Geneva Switzerland 29ndash31December 2014 pp 50ndash57 Geneva WSEAS

13 Siano D Viscardi M and Aiello R Experimental andnumerical validation of an automotive subsystem throughthe employment of FEMBEM approaches Energy Pro-cedia 2015 82 67ndash74

14 Brancati R Rocca E Lauria D Feasibility study of theHilbert transform in detecting the gear rattle phenom-enon of automotive transmissions Journal of Vibrationand Control prepublished February 1 2017 DOI1011771077546316689745

Appendix 1Notation

Ai amplitudes of the speed fluctuationcomponents (i = 1 2)

f fundamental frequency of the rattle cycler1 pitch radius of the pinion gearr2 pitch radius of the wheel gearz1 number of teeth on the pinion gearz2 number of teeth on the wheel gear

Du transmission errore transmission ratioui absolute rotations of the gears (i = 1 2)O angular speedOm mean value of the angular speed

12 Proc IMechE Part D J Automobile Engineering